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Chancellor who never gets to produce a budget??
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Keema's Nan
2020-02-13 18:50:24 UTC
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What is all that about?

Maybe an effort to get into the Guinness Records book?

Sounds a bit strange to me....
Roger
2020-02-14 09:37:31 UTC
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Post by Keema's Nan
What is all that about?
Maybe an effort to get into the Guinness Records book?
Sounds a bit strange to me....
Well it would do, must be a plot :D

With the gift of hindsight, it isn't that odd. Javid represents a competitive group within the Tory party. His original inclusion in the government was probably in order help bring on board as many groups as possible when numbers where tight.

Now they are not BJ can have a more selective team. This is normal politics....the more solid your majority the more tightly focussed you can be and do not need to compromise.

In the specific case it may well be that BJ is concerned about ending up in a Blair/Brown type situation (which one could argue is what helped the UK to get into the EU half in / half out mess in the first place).

It is not 'normal', but it is to be expected as over the next 12 months the government is going to be very focussed on getting Brexit done; it does not want extra curicular discussion or detraction.
Keema's Nan
2020-02-14 13:05:19 UTC
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Post by Roger
Post by Keema's Nan
What is all that about?
Maybe an effort to get into the Guinness Records book?
Sounds a bit strange to me....
Well it would do, must be a plot :D
Still ploughing your own yawn-inducing furrow, I see.
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.

Maybe you can enlighten us to the others?
Post by Roger
Javid represents a competitive
group within the Tory party. His original inclusion in the government was
probably in order help bring on board as many groups as possible when numbers
where tight.
Now they are not BJ can have a more selective team. This is normal
politics....the more solid your majority the more tightly focussed you can be
and do not need to compromise.
In the specific case it may well be that BJ is concerned about ending up in a
Blair/Brown type situation (which one could argue is what helped the UK to
get into the EU half in / half out mess in the first place).
It is not 'normal', but it is to be expected as over the next 12 months the
government is going to be very focussed on getting Brexit done; it does not
want extra curicular discussion or detraction.
Roger
2020-02-14 13:54:29 UTC
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Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd, which is synonymous with strange.

Perhaps you meant say it was unusual? It certainly was unusual but being as it was the child of an exceptional event (Government passing from coalition to grand majority just a few months after taking office), then perhaps that should not suprise us ;-)

For example, if the government were to conscript thousands of people into the emergency services to deal withthe aftermath of a Meteorite strike that would certainly be unusual. But given the circumstances it would not be odd or strange ;-)
Keema's Nan
2020-02-14 15:20:11 UTC
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Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Post by Roger
which is synonymous with strange.
Perhaps you meant say it was unusual?
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?

I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Post by Roger
It certainly was unusual but being as
it was the child of an exceptional event (Government passing from coalition
to grand majority just a few months after taking office), then perhaps that
should not suprise us ;-)
For example, if the government were to conscript thousands of people into the
emergency services to deal withthe aftermath of a Meteorite strike that would
certainly be unusual. But given the circumstances it would not be odd or
strange ;-)
Strawman.
Dan S. MacAbre
2020-02-14 15:57:20 UTC
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Post by Roger
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Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
Roger
2020-02-14 16:03:55 UTC
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Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
Dan S. MacAbre
2020-02-14 16:07:38 UTC
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Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
Keema's Nan
2020-02-14 16:35:10 UTC
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Post by Roger
Post by Dan S. MacAbre
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Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the
set of odd numbers then we could be talking about something that has
happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
Yes, that sums it up.
Roger
2020-02-14 23:28:02 UTC
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Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
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Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.

If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.

But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.

So we know that the infinitely large set of all integers contains one more even number than odd.

Odd isn't it?
abelard
2020-02-16 12:38:32 UTC
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Post by Roger
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
https://www.abelard.org/metalogic/metalogicA1.php
30,000 words!
--
www.abelard.org
Roger
2020-02-16 13:44:25 UTC
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Post by Roger
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Post by Roger
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Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.

It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D

But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
abelard
2020-02-16 13:47:53 UTC
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Post by abelard
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Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument

but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
--
www.abelard.org
Farmer Giles
2020-02-16 14:02:32 UTC
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Post by abelard
Post by Roger
Post by abelard
Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument
Translation: Oh dear, I've run out of bullshit, what do I do now!
Post by abelard
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
Babbelard's waffling and bullshit exposed once again.
Keema's Nan
2020-02-16 14:11:15 UTC
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Post by abelard
Post by Roger
Post by abelard
Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make
something odd,
Well that is exactly what it does make it, because it is the first
occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of
the set of odd numbers then we could be talking about something that
has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers
contains two equal infinities if Odd and Even numbers. You can have a
discrete number of infinite sets (not to mention an infinite number of
infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even
natural numbers you would have an even number of infinite sets, but if
you only had the set oven numbers you would only have and odd number of
infinite sets.
But if you had the set of odd integers and the set of even integers as
well as the set of Real numbers that would be an odd number of sets. If
you did a union of those 3 sets you would have one infinite set, but it
would not have have equal numbers of odd and even numbers because the set
of integers is comprised of an infinite number of positive integers that
is equal to the infinite number of negative integers and also
zero...which is even.
So we know that the infinitely large set of all integers contains one
more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set
means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies
empirical proof......you would run out of fingers on which to tally your
result :D
But there is a lot of stuff in maths which cannot equate to the real world,
and yet is very useful in practical calculations. The square root of minus
one springs to mind.
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
In that case, may I suggest dividing by 2?
Pancho
2020-02-16 14:14:02 UTC
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Post by abelard
Post by Roger
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Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

Didn't Anselm's "ontological proof" demonstrate the problem with this
kind of thinking. He was one of your mates, wasn't he?
Andy Walker
2020-02-16 16:19:48 UTC
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Post by Pancho
Post by abelard
Post by Roger
Post by abelard
infinity is empirically unsound
Empirically it works fine; you seem to have only philosophical
objections to it. But in any case, your problem is that you have too
restrictive a view of "infinity". The concept crops up all over the
place in mathematics, and therefore in science. Some infinities aren't
even "big"; eg, the "line at infinity" in geometry, which we all quite
happily draw as the horizon in a picture. Whether it "really is" at
infinity is irrelevant.

[...]
Post by Pancho
Post by abelard
Post by Roger
But there is a lot of stuff in maths which cannot equate to the
real world, and yet is very useful in practical calculations. The
square root of minus one springs to mind.
It's a misconception that sqrt(-1) "cannot equate to the real
world", arising from the misuse of "real", "imaginary" and "complex"
to describe certain numbers. Sqrt(-1) is a perfectly normal point in
an Argand diagram; it just requires a different view of the notion
of "multiplication" from the one you learn as a small child, but one
which maps onto that notion in simple cases.
Post by Pancho
Post by abelard
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
You can't sensibly teach "larners" that way. A smart-Alick
4yo is bound to ask you what happens to this number [which *my*
smart-Alick 4yo invented for herself and called, for no reason we
ever discovered, "kwess"] if you add one to it, or whether it's odd
or even or prime or ...; you finish up with more questions than
answers, and you can't answer them in a satisfactory way. There
are reasons why we discovered the different sorts of number in the
order we did, and you can't buck that process without causing much
worse problems.

OTOH, it would have been perfectly possible to discover
mathematics in a slightly different, more operational, way. For
example, in game theory, moves form a natural primitive currency;
and "infinity" corresponds to a blank cheque. So if I have a
blank cheque, then all I need to do to win is to fill it in with
more moves than you possess and cash it; in real life, quite a
modest sum often suffices, perhaps less than 10, very likely less
than 1000000, but larger numbers are available if needed. Such
an "infinity" has some, but not all, of the properties of more
conventional numbers; it's a number, but not as we know it, Jim.
Life then gets more interesting if you also have a blank cheque;
then whoever is forced to fill in his cheque first loses. After
that, there is a whole arithmetic of blank cheques, in case we
each have several, or even an arbitrary number, and of "entailed"
cheques [worth "infinity/2", or "sqrt(infinity)", ...], and another
arithmetic of "infinitesimal" cheques.
Post by Pancho
So how many natural numbers should we tell learners there are.
Is this number also the biggest natural number?
What makes you think that the answer to "how many?"
questions has to be a natural number? But that's a question of
philosophy rather than of mathematics. We have only one Real
World, but many ways of describing it, and many different ways
to extend mathematics beyond "1, 2, 3, ..." to a powerful tool
to use in those descriptions. Or just to enjoy.
--
Andy Walker,
Nottingham.
Roger
2020-02-16 16:26:43 UTC
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Post by Andy Walker
It's a misconception that sqrt(-1) "cannot equate to the real
world",
So how would Euclid have described it?
Keema's Nan
2020-02-16 17:15:31 UTC
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Post by Roger
Post by Andy Walker
It's a misconception that sqrt(-1) "cannot equate to the real
world",
So how would Euclid have described it?
άπειρο, αχανές
Roger
2020-02-16 17:59:12 UTC
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Post by Roger
Post by Andy Walker
It's a misconception that sqrt(-1) "cannot equate to the real
world",
So how would Euclid have described it?
OK, I'm going to withdraw this post....thinking about it Andy is right!

After all, Euclid would have had no problem with the area of a square whatever quadrant of a Cartesian graph you drew it in.
Andy Walker
2020-02-16 18:22:24 UTC
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Post by Roger
OK, I'm going to withdraw this post....thinking about it Andy is right!
Always a good starting point.
--
Andy Walker,
Nottingham.
Farmer Giles
2020-02-16 16:27:40 UTC
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Post by Pancho
Post by abelard
Post by Roger
Post by abelard
infinity is empirically unsound
    Empirically it works fine;  you seem to have only philosophical
objections to it.  But in any case, your problem is that you have too
restrictive a view of "infinity".  The concept crops up all over the
place in mathematics, and therefore in science.  Some infinities aren't
even "big";  eg, the "line at infinity" in geometry, which we all quite
happily draw as the horizon in a picture.  Whether it "really is" at
infinity is irrelevant.
[...]
Post by Pancho
Post by abelard
Post by Roger
But there is a lot of stuff in maths which cannot equate to the
real world, and yet is very useful in practical calculations. The
square root of minus one springs to mind.
    It's a misconception that sqrt(-1) "cannot equate to the real
world", arising from the misuse of "real", "imaginary" and "complex"
to describe certain numbers.  Sqrt(-1) is a perfectly normal point in
an Argand diagram;  it just requires a different view of the notion
of "multiplication" from the one you learn as a small child, but one
which maps onto that notion in simple cases.
Post by Pancho
Post by abelard
no argument
but i'd rather that instead of 'infinity' larners were taught to use
some arbitrary large number
    You can't sensibly teach "larners" that way.  A smart-Alick
4yo is bound to ask you what happens to this number [which *my*
smart-Alick 4yo invented for herself and called, for no reason we
ever discovered, "kwess"] if you add one to it, or whether it's odd
or even or prime or ...;  you finish up with more questions than
answers, and you can't answer them in a satisfactory way.  There
are reasons why we discovered the different sorts of number in the
order we did, and you can't buck that process without causing much
worse problems.
    OTOH, it would have been perfectly possible to discover
mathematics in a slightly different, more operational, way.  For
example, in game theory, moves form a natural primitive currency;
and "infinity" corresponds to a blank cheque.  So if I have a
blank cheque, then all I need to do to win is to fill it in with
more moves than you possess and cash it;  in real life, quite a
modest sum often suffices, perhaps less than 10, very likely less
than 1000000, but larger numbers are available if needed.  Such
an "infinity" has some, but not all, of the properties of more
conventional numbers;  it's a number, but not as we know it, Jim.
Life then gets more interesting if you also have a blank cheque;
then whoever is forced to fill in his cheque first loses.  After
that, there is a whole arithmetic of blank cheques, in case we
each have several, or even an arbitrary number, and of "entailed"
cheques [worth "infinity/2", or "sqrt(infinity)", ...], and another
arithmetic of "infinitesimal" cheques.
Post by Pancho
So how many natural numbers should we tell learners there are.
Is this number also the biggest natural number?
    What makes you think that the answer to "how many?"
questions has to be a natural number?  But that's a question of
philosophy rather than of mathematics.  We have only one Real
World, but many ways of describing it, and many different ways
to extend mathematics beyond "1, 2, 3, ..." to a powerful tool
to use in those descriptions.  Or just to enjoy.
This would have been a very good post if you hadn't mixed up whom you
were replying to. The person you appear to be replying to didn't say
some of the things you have answered.
Andy Walker
2020-02-16 18:29:49 UTC
Reply
Permalink
Post by Farmer Giles
This would have been a very good post if you hadn't mixed up whom you
were replying to. The person you appear to be replying to didn't say
some of the things you have answered.
*I* didn't mix it up, and nor did the software on my computer.
I was responding to a thread with three relevant previous contributors
[Abelard twice], all named near the top of my post, and distinguished,
as is the Usenet convention, by the number of ">"'s at the start of
each line. You've surely been writing articles for long enough to
understand all that? The alternative would have been to write four
separate articles, with corresponding difficulties in connecting the
points made to each other.
--
Andy Walker,
Nottingham.
abelard
2020-02-16 17:25:32 UTC
Reply
Permalink
Post by Andy Walker
Post by Pancho
Post by abelard
Post by Roger
Post by abelard
infinity is empirically unsound
Empirically it works fine; you seem to have only philosophical
objections to it. But in any case, your problem is that you have too
restrictive a view of "infinity". The concept crops up all over the
place in mathematics, and therefore in science. Some infinities aren't
even "big"; eg, the "line at infinity" in geometry, which we all quite
happily draw as the horizon in a picture. Whether it "really is" at
infinity is irrelevant.
[...]
Post by Pancho
Post by abelard
Post by Roger
But there is a lot of stuff in maths which cannot equate to the
real world, and yet is very useful in practical calculations. The
square root of minus one springs to mind.
It's a misconception that sqrt(-1) "cannot equate to the real
world", arising from the misuse of "real", "imaginary" and "complex"
to describe certain numbers. Sqrt(-1) is a perfectly normal point in
an Argand diagram; it just requires a different view of the notion
of "multiplication" from the one you learn as a small child, but one
which maps onto that notion in simple cases.
Post by Pancho
Post by abelard
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
You can't sensibly teach "larners" that way. A smart-Alick
4yo is bound to ask you what happens to this number [which *my*
smart-Alick 4yo invented for herself and called, for no reason we
ever discovered, "kwess"] if you add one to it, or whether it's odd
or even or prime or ...; you finish up with more questions than
answers, and you can't answer them in a satisfactory way. There
are reasons why we discovered the different sorts of number in the
order we did, and you can't buck that process without causing much
worse problems.
i'm all for 4yos asking questions
Post by Andy Walker
OTOH, it would have been perfectly possible to discover
mathematics in a slightly different, more operational, way. For
example, in game theory, moves form a natural primitive currency;
and "infinity" corresponds to a blank cheque. So if I have a
blank cheque, then all I need to do to win is to fill it in with
more moves than you possess and cash it; in real life, quite a
modest sum often suffices, perhaps less than 10, very likely less
than 1000000, but larger numbers are available if needed. Such
an "infinity" has some, but not all, of the properties of more
conventional numbers; it's a number, but not as we know it, Jim.
Life then gets more interesting if you also have a blank cheque;
then whoever is forced to fill in his cheque first loses. After
that, there is a whole arithmetic of blank cheques, in case we
each have several, or even an arbitrary number, and of "entailed"
cheques [worth "infinity/2", or "sqrt(infinity)", ...], and another
arithmetic of "infinitesimal" cheques.
Post by Pancho
So how many natural numbers should we tell learners there are.
Is this number also the biggest natural number?
it is a personal choice...i prefer that, to your authoritarian
approach
Post by Andy Walker
What makes you think that the answer to "how many?"
questions has to be a natural number? But that's a question of
philosophy rather than of mathematics. We have only one Real
World, but many ways of describing it, and many different ways
to extend mathematics beyond "1, 2, 3, ..." to a powerful tool
to use in those descriptions. Or just to enjoy.
--
www.abelard.org
Andy Walker
2020-02-16 18:40:20 UTC
Reply
Permalink
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
--
Andy Walker,
Nottingham.
Keema's Nan
2020-02-16 19:34:57 UTC
Reply
Permalink
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
Yes, my granddaughter said the other day “I can’t get married when I get
older”.

When I asked why that might be, she replied “married people have babies and
I don’t know how to make one”.

I suggested tactfully that she would find out all about that when she was
older, and that I thought she should not worry about those things at her age
- she is 5.
Ophelia
2020-02-17 10:00:42 UTC
Reply
Permalink
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
Yes, my granddaughter said the other day “I can’t get married when I get
older”.

When I asked why that might be, she replied “married people have babies and
I don’t know how to make one”.

I suggested tactfully that she would find out all about that when she was
older, and that I thought she should not worry about those things at her age
- she is 5.

===

She is a thinker:))
abelard
2020-02-16 19:46:48 UTC
Reply
Permalink
Post by Andy Walker
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
imv i'm very content that a 4yo decides what kwess is...i encourage
them to explain it to me...

i'm also happy they deal with 'setbacks'...that helps them deal with
real life....'setbacks' are opportunities...'setbacks' are puzzles
to encourage curiosity...

i'm very happy they try to run before they walk, for similar reasons

i don't quite see your difficulties
--
www.abelard.org
Andy Walker
2020-02-16 21:00:26 UTC
Reply
Permalink
Post by abelard
Post by Andy Walker
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Post by abelard
Post by Andy Walker
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
imv i'm very content that a 4yo decides what kwess is...i encourage
them to explain it to me...
i'm also happy they deal with 'setbacks'...that helps them deal with
real life....'setbacks' are opportunities...'setbacks' are puzzles
to encourage curiosity...
i'm very happy they try to run before they walk, for similar reasons
i don't quite see your difficulties
Perhaps the bit I've emphasised above will help? I broadly
agree with you, but there is a fine line between setbacks that cause
youngsters to explore further and setbacks that cause them to lose
heart and interest. You need to feel that you're making progress.
--
Andy Walker,
Nottingham.
abelard
2020-02-16 23:30:32 UTC
Reply
Permalink
Post by Andy Walker
Post by abelard
Post by Andy Walker
Post by abelard
i'm all for 4yos asking questions
So am I. But often the only good answer is "I can't answer
that until you're 16 and have learned enough history/physics/...
for this to make sense". Too much of that is a Bad Thing, tho' 4yos
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Post by abelard
Post by Andy Walker
can cope with occasional setbacks of that sort. As previously, there
are reasons why science [inc maths, philosophy, etc] was discovered
in a particular order, and we need to walk before we run.
imv i'm very content that a 4yo decides what kwess is...i encourage
them to explain it to me...
i'm also happy they deal with 'setbacks'...that helps them deal with
real life....'setbacks' are opportunities...'setbacks' are puzzles
to encourage curiosity...
i'm very happy they try to run before they walk, for similar reasons
i don't quite see your difficulties
Perhaps the bit I've emphasised above will help? I broadly
agree with you, but there is a fine line between setbacks that cause
youngsters to explore further and setbacks that cause them to lose
heart and interest. You need to feel that you're making progress.
i'm content to stipulate that much depends on prior upbringing

i don't think snowflakery does young people many favours
--
www.abelard.org
Pancho
2020-02-16 18:09:22 UTC
Reply
Permalink
Post by Pancho
Post by abelard
Post by Roger
Post by abelard
infinity is empirically unsound
    Empirically it works fine;  you seem to have only philosophical
objections to it.  But in any case, your problem is that you have too
restrictive a view of "infinity".  The concept crops up all over the
place in mathematics, and therefore in science.  Some infinities aren't
even "big";  eg, the "line at infinity" in geometry, which we all quite
happily draw as the horizon in a picture.  Whether it "really is" at
infinity is irrelevant.
[...]
Post by Pancho
Post by abelard
Post by Roger
But there is a lot of stuff in maths which cannot equate to the
real world, and yet is very useful in practical calculations. The
square root of minus one springs to mind.
    It's a misconception that sqrt(-1) "cannot equate to the real
world", arising from the misuse of "real", "imaginary" and "complex"
to describe certain numbers.  Sqrt(-1) is a perfectly normal point in
an Argand diagram;  it just requires a different view of the notion
of "multiplication" from the one you learn as a small child, but one
which maps onto that notion in simple cases.
Post by Pancho
Post by abelard
no argument
but i'd rather that instead of 'infinity' larners were taught to use
some arbitrary large number
    You can't sensibly teach "larners" that way.  A smart-Alick
4yo is bound to ask you what happens to this number [which *my*
smart-Alick 4yo invented for herself and called, for no reason we
ever discovered, "kwess"] if you add one to it, or whether it's odd
or even or prime or ...;  you finish up with more questions than
answers, and you can't answer them in a satisfactory way.  There
are reasons why we discovered the different sorts of number in the
order we did, and you can't buck that process without causing much
worse problems.
    OTOH, it would have been perfectly possible to discover
mathematics in a slightly different, more operational, way.  For
example, in game theory, moves form a natural primitive currency;
and "infinity" corresponds to a blank cheque.  So if I have a
blank cheque, then all I need to do to win is to fill it in with
more moves than you possess and cash it;  in real life, quite a
modest sum often suffices, perhaps less than 10, very likely less
than 1000000, but larger numbers are available if needed.  Such
an "infinity" has some, but not all, of the properties of more
conventional numbers;  it's a number, but not as we know it, Jim.
Life then gets more interesting if you also have a blank cheque;
then whoever is forced to fill in his cheque first loses.  After
that, there is a whole arithmetic of blank cheques, in case we
each have several, or even an arbitrary number, and of "entailed"
cheques [worth "infinity/2", or "sqrt(infinity)", ...], and another
arithmetic of "infinitesimal" cheques.
Post by Pancho
So how many natural numbers should we tell learners there are.
Is this number also the biggest natural number?
    What makes you think that the answer to "how many?"
questions has to be a natural number?
I don't, indeed, I was taught the answer was aleph-0, which is not a
Natural number. Perhaps your objection is that I should have used
capital N in Natural?

But following from the Peano axioms and the concept of successor if the
Natural numbers were finite, wouldn't we expect that the biggest one
would also be the cardinality.
But that's a question of
philosophy rather than of mathematics.
I don't see why, I thought Cantor nailed it, in mathematics.
Andy Walker
2020-02-16 19:16:02 UTC
Reply
Permalink
Post by Pancho
Post by Pancho
So how many natural numbers should we tell learners there are.
Is this number also the biggest natural number?
     What makes you think that the answer to "how many?"
questions has to be a natural number?
I don't, indeed, I was taught the answer was aleph-0, which is not a
Natural number. Perhaps your objection is that I should have used
capital N in Natural?
No; and I didn't raise an objection, merely a query. The
trouble is that "learner" covers 4yos, PhD students, and all points
between and beyond, and there is no one answer. "Aleph-0" is not
a suitable answer for 4yos, and it's not even a good answer for
sixth formers or thereabouts; it's just an invented name for the
concept, it doesn't convey any useful information. The useful bit
comes when you find that lots of other sets can be paired off with
the naturals, so that you have a notation for a much wider concept
[and that other sets cannot be so paired, giving you the basis for
some surprising developments].
Post by Pancho
But following from the Peano axioms and the concept of successor if
the Natural numbers were finite, wouldn't we expect that the biggest
one would also be the cardinality.
What makes you think .... Look, the problem is that maths
is usually taught in the authoritarian way that Abelard correctly
objects to. The result is that students think that maths is *the*
subject in which answers are right or wrong, black or white, with
no shades of grey. Sadly, teachers and even university maths
lecturers all too often think the same way. The truth is that
any study of the history of maths [now part of many curriculums,
but that's a recent development] shows a series of revolutions,
by which "self-evident truths" turn out to be not quite as self-
evident as they once seemed, so that concepts that used to be
ridiculed become mainstream. Equally, maths is, much more than
is popularly supposed, substantially a matter of fashion. I was
at a conference a while back where a lecturer from Warwick said
that he gave a complete module on abandoned ideas from 19thC
geometry.
Post by Pancho
But that's a question of
philosophy rather than of mathematics.
I don't see why, I thought Cantor nailed it, in mathematics.
He did. Just as Euclid nailed geometry, Newton nailed
mechanics, and Cauchy nailed analysis. But you nail things based
on particular axioms, and it's the nature of axioms that they
fall apart if you ask whether or not they are true. They are
true *by self-evident assumption*, so that as soon as anyone
seriously questions them they stop being self-evident. IRL,
Newton and Euclid survive pretty well despite now being debunked,
ie as long as you are only concerned with cases where the axioms
are sufficiently-nearly true. So, are the Peano axioms *true*?
Well, yes, they're self-evidently true. OTOH, perhaps ...; and
that's where we get into philosophy.
--
Andy Walker,
Nottingham.
abelard
2020-02-16 17:21:55 UTC
Reply
Permalink
On Sun, 16 Feb 2020 14:14:02 +0000, Pancho
Post by Pancho
Post by abelard
Post by Roger
Post by abelard
Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So how many natural numbers should we tell learners there are.
it doesn't matter..just pick one according to taste and purpose
Post by Pancho
Is this number also the biggest natural number?
Didn't Anselm's "ontological proof" demonstrate the problem with this
kind of thinking. He was one of your mates, wasn't he?
https://www.abelard.org/heresies/heresies.htm#greater-than
A dictionary defines ‘ontology’ as ‘the branch of metaphysics dealing
with the nature of being’, while that for metaphysics is ‘the
theoretical philosophy of being and knowing’ or ‘the philosophy of
mind’. ‘Being’, the explanation continues, is existence or the nature
or essence (of a person etc.), ‘mind’ is the seat of consciousness,
thought, volition, feeling, the intellect; intellectual powers and
more. And so it will go with ‘philosophy’, ‘knowing’, ‘existence’, in
exquisite circles of self-referring and rather empty words. Little
wonder that Roscelin of Compiegne, a teacher of Abelard, called words
mere farts (flatus vocis).

The ontological argument proceeds, not empirically from the world, but
from the ‘idea’ of ‘God’ to the ‘reality’ of God. It was first
formulated by ‘St.’ Anselm of Canterbury (1033 or 1034 – 1109) in his
Proslogion (1077 – 1078). Anselm began with the concept of God as
being that than which nothing greater can be conceived (aliquid quo
nihil majus cogitari possit). Note the distinctly mathematical nature
of this approach. I sit upon a rock, it is likely that there be a
larger rock elsewhere and an even larger rock beyond that.

The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.

more at link
--
www.abelard.org
Pancho
2020-02-16 18:07:56 UTC
Reply
Permalink
Post by abelard
On Sun, 16 Feb 2020 14:14:02 +0000, Pancho
Post by Pancho
Post by abelard
Post by Roger
Post by abelard
Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So how many natural numbers should we tell learners there are.
it doesn't matter..just pick one according to taste and purpose
Post by Pancho
Is this number also the biggest natural number?
Didn't Anselm's "ontological proof" demonstrate the problem with this
kind of thinking. He was one of your mates, wasn't he?
https://www.abelard.org/heresies/heresies.htm#greater-than
A dictionary defines ‘ontology’ as ‘the branch of metaphysics dealing
with the nature of being’, while that for metaphysics is ‘the
theoretical philosophy of being and knowing’ or ‘the philosophy of
mind’. ‘Being’, the explanation continues, is existence or the nature
or essence (of a person etc.), ‘mind’ is the seat of consciousness,
thought, volition, feeling, the intellect; intellectual powers and
more. And so it will go with ‘philosophy’, ‘knowing’, ‘existence’, in
exquisite circles of self-referring and rather empty words. Little
wonder that Roscelin of Compiegne, a teacher of Abelard, called words
mere farts (flatus vocis).
The ontological argument proceeds, not empirically from the world, but
from the ‘idea’ of ‘God’ to the ‘reality’ of God. It was first
formulated by ‘St.’ Anselm of Canterbury (1033 or 1034 – 1109) in his
Proslogion (1077 – 1078). Anselm began with the concept of God as
being that than which nothing greater can be conceived (aliquid quo
nihil majus cogitari possit). Note the distinctly mathematical nature
of this approach. I sit upon a rock, it is likely that there be a
larger rock elsewhere and an even larger rock beyond that.
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine. The flaw is that he assumes the existence of
a "greatest thing that can be conceived". This is very similar to
conceiving of a biggest natural number.
abelard
2020-02-16 19:50:24 UTC
Reply
Permalink
On Sun, 16 Feb 2020 18:07:56 +0000, Pancho
Post by Pancho
Post by abelard
On Sun, 16 Feb 2020 14:14:02 +0000, Pancho
Post by Pancho
Post by abelard
Post by Roger
Post by abelard
Post by Roger
Post by Dan S. MacAbre
Post by Roger
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
I suppose if we restrict the use of the word odd to being a member of the set of odd numbers then we could be talking about something that has happened 10000000000000001 times!
You know, I have to wonder whether infinity is regarded as an odd or an
even number. If it's neither, then that's even odder.
I think Infinity is regarded as a set. The Set of natural numbers contains two equal infinities if Odd and Even numbers. You can have a discrete number of infinite sets (not to mention an infinite number of infinities), so you can have odd even numbers of infinite sets.
If you took the set of all odd natural numbers and the set of all even natural numbers you would have an even number of infinite sets, but if you only had the set oven numbers you would only have and odd number of infinite sets.
But if you had the set of odd integers and the set of even integers as well as the set of Real numbers that would be an odd number of sets. If you did a union of those 3 sets you would have one infinite set, but it would not have have equal numbers of odd and even numbers because the set of integers is comprised of an infinite number of positive integers that is equal to the infinite number of negative integers and also zero...which is even.
So we know that the infinitely large set of all integers contains one more even number than odd.
Odd isn't it?
infinity is empirically unsound
In terms of mathematical sets of numbers, the term infinite uncountable set means a set which is larger than the set of Natural numbers.
It is therefore almost tautological to state that it's existence defies empirical proof......you would run out of fingers on which to tally your result :D
But there is a lot of stuff in maths which cannot equate to the real world, and yet is very useful in practical calculations. The square root of minus one springs to mind.
no argument
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So how many natural numbers should we tell learners there are.
it doesn't matter..just pick one according to taste and purpose
Post by Pancho
Is this number also the biggest natural number?
Didn't Anselm's "ontological proof" demonstrate the problem with this
kind of thinking. He was one of your mates, wasn't he?
https://www.abelard.org/heresies/heresies.htm#greater-than
A dictionary defines ‘ontology’ as ‘the branch of metaphysics dealing
with the nature of being’, while that for metaphysics is ‘the
theoretical philosophy of being and knowing’ or ‘the philosophy of
mind’. ‘Being’, the explanation continues, is existence or the nature
or essence (of a person etc.), ‘mind’ is the seat of consciousness,
thought, volition, feeling, the intellect; intellectual powers and
more. And so it will go with ‘philosophy’, ‘knowing’, ‘existence’, in
exquisite circles of self-referring and rather empty words. Little
wonder that Roscelin of Compiegne, a teacher of Abelard, called words
mere farts (flatus vocis).
The ontological argument proceeds, not empirically from the world, but
from the ‘idea’ of ‘God’ to the ‘reality’ of God. It was first
formulated by ‘St.’ Anselm of Canterbury (1033 or 1034 – 1109) in his
Proslogion (1077 – 1078). Anselm began with the concept of God as
being that than which nothing greater can be conceived (aliquid quo
nihil majus cogitari possit). Note the distinctly mathematical nature
of this approach. I sit upon a rock, it is likely that there be a
larger rock elsewhere and an even larger rock beyond that.
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Post by Pancho
The flaw is that he assumes the existence of
a "greatest thing that can be conceived". This is very similar to
conceiving of a biggest natural number.
that sounds plausible at this moment to me!
--
www.abelard.org
Pancho
2020-02-17 00:43:57 UTC
Reply
Permalink
Post by abelard
Post by Pancho
Post by abelard
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Mathematically an argument similar to Anselm's might be to prove a
Natural number N exists for which some of the rules of arithmetic do not
apply.

Proof:

Conceive the greatest Natural number, call it N.
Assume the rules of arithmetic apply to N.
Therefore N+1 > N
Therefore N+1 (not N) is the greatest Natural number.

So we have a contradiction with N being the greatest Natural number. By
contradiction (reductio ad absurdum) our assumption that the rules of
arithmetic apply to N must be false.

QED

If a greatest Natural number N existed, the proof would be valid, but
the flaw is that a greatest Natural number does not exist, we have
implicitly assumed its existence, just as Anselm implicitly assumed we
could conceive a greatest thing.
abelard
2020-02-17 12:54:29 UTC
Reply
Permalink
On Mon, 17 Feb 2020 00:43:57 +0000, Pancho
Post by Pancho
Post by abelard
Post by Pancho
Post by abelard
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Mathematically an argument similar to Anselm's might be to prove a
Natural number N exists for which some of the rules of arithmetic do not
apply.
Conceive the greatest Natural number, call it N.
Assume the rules of arithmetic apply to N.
Therefore N+1 > N
Therefore N+1 (not N) is the greatest Natural number.
So we have a contradiction with N being the greatest Natural number. By
contradiction (reductio ad absurdum) our assumption that the rules of
arithmetic apply to N must be false.
QED
If a greatest Natural number N existed, the proof would be valid, but
the flaw is that a greatest Natural number does not exist, we have
implicitly assumed its existence, just as Anselm implicitly assumed we
could conceive a greatest thing.
there are so many problems...

i have the biggest truck in the world but the neighbour has
stuck chewing gum on hers to make it heavier...

yesterday the biggest number was enormous..now it's even
bigger

notice in each case time moved on....missing the time stamp
avoids reality..


or you could run out of ink or die before you had time to count on
--
www.abelard.org
Keema's Nan
2020-02-17 13:26:49 UTC
Reply
Permalink
Post by abelard
On Mon, 17 Feb 2020 00:43:57 +0000, Pancho
Post by Pancho
Post by abelard
Post by Pancho
Post by abelard
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Mathematically an argument similar to Anselm's might be to prove a
Natural number N exists for which some of the rules of arithmetic do not
apply.
Conceive the greatest Natural number, call it N.
Assume the rules of arithmetic apply to N.
Therefore N+1 > N
Therefore N+1 (not N) is the greatest Natural number.
So we have a contradiction with N being the greatest Natural number. By
contradiction (reductio ad absurdum) our assumption that the rules of
arithmetic apply to N must be false.
QED
If a greatest Natural number N existed, the proof would be valid, but
the flaw is that a greatest Natural number does not exist, we have
implicitly assumed its existence, just as Anselm implicitly assumed we
could conceive a greatest thing.
there are so many problems...
The main one being those who like to show off their mathematical expertise,
really just expose their ignorance.

Infinity is undefined, and will remain so until..... er, infinity
Post by abelard
i have the biggest truck in the world but the neighbour has
stuck chewing gum on hers to make it heavier...
yesterday the biggest number was enormous..now it's even
bigger
notice in each case time moved on....missing the time stamp
avoids reality..
or you could run out of ink or die before you had time to count on
Pancho
2020-02-17 15:16:21 UTC
Reply
Permalink
Post by Keema's Nan
Post by abelard
On Mon, 17 Feb 2020 00:43:57 +0000, Pancho
Post by Pancho
Post by abelard
Post by Pancho
Post by abelard
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Mathematically an argument similar to Anselm's might be to prove a
Natural number N exists for which some of the rules of arithmetic do not
apply.
Conceive the greatest Natural number, call it N.
Assume the rules of arithmetic apply to N.
Therefore N+1 > N
Therefore N+1 (not N) is the greatest Natural number.
So we have a contradiction with N being the greatest Natural number. By
contradiction (reductio ad absurdum) our assumption that the rules of
arithmetic apply to N must be false.
QED
If a greatest Natural number N existed, the proof would be valid, but
the flaw is that a greatest Natural number does not exist, we have
implicitly assumed its existence, just as Anselm implicitly assumed we
could conceive a greatest thing.
there are so many problems...
The main one being those who like to show off their mathematical expertise,
really just expose their ignorance.
Isn't that true of all subjects. From my own perspective, I like people
to show me up. Much better to be corrected here, rather than exposed as
a fool in real life. ;o)
Post by Keema's Nan
Infinity is undefined, and will remain so until..... er, infinity
Infinity is relatively well defined. Well enough defined that we even
have to distinguish between at least two different types of infinity.

Or at least we do distinguish, for theoretical completeness. I'm not
sure if we actually do need to distinguish for practical purposes. It's
hard for me to unpick what I have been taught to know where I actually
need infinity and where it can be avoided.
Keema's Nan
2020-02-17 16:54:22 UTC
Reply
Permalink
Post by Pancho
Post by Keema's Nan
Post by abelard
On Mon, 17 Feb 2020 00:43:57 +0000, Pancho
Post by Pancho
Post by abelard
Post by Pancho
Post by abelard
The argument goes: To think of such a being as existing only in
thought and not also in reality involves a contradiction (see also
excluded middle). This jump is equivalent to suggesting that if I can
think of a dog with 17.5 heads, to suggest that such a dog does not
‘exist’ involves a ‘contradiction’. However, the notion of
‘contradiction’ is weakly based, especially when it is not subject
to
clear negotiated definitions or to empirical testing.
The contradiction is fine.
why is it 'fine'...how do you get a 'contradiction' with that
which does not exist?
Mathematically an argument similar to Anselm's might be to prove a
Natural number N exists for which some of the rules of arithmetic do not
apply.
Conceive the greatest Natural number, call it N.
Assume the rules of arithmetic apply to N.
Therefore N+1 > N
Therefore N+1 (not N) is the greatest Natural number.
So we have a contradiction with N being the greatest Natural number. By
contradiction (reductio ad absurdum) our assumption that the rules of
arithmetic apply to N must be false.
QED
If a greatest Natural number N existed, the proof would be valid, but
the flaw is that a greatest Natural number does not exist, we have
implicitly assumed its existence, just as Anselm implicitly assumed we
could conceive a greatest thing.
there are so many problems...
The main one being those who like to show off their mathematical expertise,
really just expose their ignorance.
Isn't that true of all subjects. From my own perspective, I like people
to show me up. Much better to be corrected here, rather than exposed as
a fool in real life. ;o)
Post by Keema's Nan
Infinity is undefined, and will remain so until..... er, infinity
Infinity is relatively well defined.
And yet you seemed to have failed to define it, mathematically that is....

In other words, not just - infinity is the quality of being infinite.
Post by Pancho
Well enough defined that we even
have to distinguish between at least two different types of infinity.
Or even an infinite number of infinities.
Post by Pancho
Or at least we do distinguish, for theoretical completeness. I'm not
sure if we actually do need to distinguish for practical purposes. It's
hard for me to unpick what I have been taught to know where I actually
need infinity and where it can be avoided.
Roger
2020-02-16 15:26:25 UTC
Reply
Permalink
Post by abelard
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So kiddies, don't divide by zero or you'll end up with the national debt.
abelard
2020-02-16 17:27:25 UTC
Reply
Permalink
Post by Roger
Post by abelard
but i'd rather that instead of 'infinity' larners were taught to
use some arbitrary large number
So kiddies, don't divide by zero or you'll end up with the national debt.
division by zero is undefined

it is you damn commies that end up with infinity...for the
national debt...

i'm very 'excited' to see what boris will make of it!
--
www.abelard.org
Keema's Nan
2020-02-14 16:08:41 UTC
Reply
Permalink
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
Yes, but he has no concept of humour or (seemingly) irony.
Dan S. MacAbre
2020-02-14 16:12:37 UTC
Reply
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Post by Keema's Nan
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Post by Roger
With the gift of hindsight, it isn't that odd.
It is, because I can’t think of another occasion when it happened.
Lack of prior art makes something unusual, it does not make something odd,
Well that is exactly what it does make it, because it is the first occasion
in many centuries and 1 is an odd number.
Then it would also be 'unique' :-)
Yes, but he has no concept of humour or (seemingly) irony.
I suppose irony can be a bit tricky on usenet.
Roger
2020-02-14 15:59:33 UTC
Reply
Permalink
Post by Keema's Nan
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?
I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Just to recap, it was you who took me to task for saying it wasn't odd.
Keema's Nan
2020-02-14 16:07:25 UTC
Reply
Permalink
Post by Roger
Post by Keema's Nan
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?
I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Just to recap, it was you who took me to task for saying it wasn't odd.
Another attempt at a patronising put down.

I am well aware of my previous posts, thanks - and I provided my thicko
reasoning for you to pull to pieces.
Dan S. MacAbre
2020-02-14 16:10:42 UTC
Reply
Permalink
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?
I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Just to recap, it was you who took me to task for saying it wasn't odd.
Another attempt at a patronising put down.
I am well aware of my previous posts, thanks - and I provided my thicko
reasoning for you to pull to pieces.
Can I respectfully suggest that you need to work on your self-esteem? :-)
Keema's Nan
2020-02-14 16:35:55 UTC
Reply
Permalink
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?
I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Just to recap, it was you who took me to task for saying it wasn't odd.
Another attempt at a patronising put down.
I am well aware of my previous posts, thanks - and I provided my thicko
reasoning for you to pull to pieces.
Can I respectfully suggest that you need to work on your self-esteem? :-)
Yes you can.
Keema's Nan
2020-02-15 13:58:30 UTC
Reply
Permalink
Post by Keema's Nan
Post by Dan S. MacAbre
Post by Keema's Nan
Post by Roger
Post by Keema's Nan
Perhaps you would care to stick your arrogance in a drawer, or at least
somewhere the sun doesn’t shine?
I don’t react kindly to patronising comments; but that might be why you
make them - just for sport with those who you deem far below your
intellectual level.
Just to recap, it was you who took me to task for saying it wasn't odd.
Another attempt at a patronising put down.
I am well aware of my previous posts, thanks - and I provided my thicko
reasoning for you to pull to pieces.
Can I respectfully suggest that you need to work on your self-esteem? :-)
Yes you can.
However, that is not particularly easy for someone trying to recover from an
alcohol addiction.
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