Keema's Nan

2020-02-13 18:50:24 UTC

Reply

PermalinkMaybe an effort to get into the Guinness Records book?

Sounds a bit strange to me....

Discussion:

Add Reply

Keema's Nan

2020-02-13 18:50:24 UTC

Reply

PermalinkMaybe an effort to get into the Guinness Records book?

Sounds a bit strange to me....

Roger

2020-02-14 09:37:31 UTC

Reply

PermalinkWhat is all that about?

Maybe an effort to get into the Guinness Records book?

Sounds a bit strange to me....

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

Reply

PermalinkWhat is all that about?

Maybe an effort to get into the Guinness Records book?

Sounds a bit strange to me....

It is, because I can’t think of another occasion when it happened.

Maybe you can enlighten us to the others?

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

Reply

PermalinkPerhaps 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

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

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.

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 ;-)

Dan S. MacAbre

2020-02-14 15:57:20 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

Roger

2020-02-14 16:03:55 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

Dan S. MacAbre

2020-02-14 16:07:38 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

Keema's Nan

2020-02-14 16:35:10 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

set of odd numbers then we could be talking about something that has

happened 10000000000000001 times!

even number. If it's neither, then that's even odder.

Roger

2020-02-14 23:28:02 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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

Reply

PermalinkIt is, because I cant think of another occasion when it happened.

Lack of prior art makes something unusual, it does not make something odd,in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

https://www.abelard.org/metalogic/metalogicA1.php

30,000 words!

--

www.abelard.org

www.abelard.org

Roger

2020-02-16 13:44:25 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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

Reply

PermalinkIt is, because I cant think of another occasion when it happened.

Lack of prior art makes something unusual, it does not make something odd,in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

--

www.abelard.org

www.abelard.org

Farmer Giles

2020-02-16 14:02:32 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

Keema's Nan

2020-02-16 14:11:15 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make

something odd,

occasion

in many centuries and 1 is an odd number.

the set of odd numbers then we could be talking about something that

has happened 10000000000000001 times!

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

Pancho

2020-02-16 14:14:02 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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

Reply

Permalinkobjections 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.

[...]

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.

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.

no argument

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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.

So how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

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.

Andy Walker,

Nottingham.

Roger

2020-02-16 16:26:43 UTC

Reply

Permalink
Keema's Nan

2020-02-16 17:15:31 UTC

Roger

2020-02-16 17:59:12 UTC

Reply

PermalinkAfter 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

Farmer Giles

2020-02-16 16:27:40 UTC

Reply

Permalink 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 youobjections 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.

[...]

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.

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.

no argument

but i'd rather that instead of 'infinity' larners were taught to use

some arbitrary large number

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.

So how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

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.

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

PermalinkThis 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 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.

Andy Walker,

Nottingham.

abelard

2020-02-16 17:25:32 UTC

Reply

PermalinkEmpirically 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.

[...]

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.

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.

no argument

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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.

So how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

approach

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

www.abelard.org

Andy Walker

2020-02-16 18:40:20 UTC

Reply

Permalinkthat 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.

Andy Walker,

Nottingham.

Keema's Nan

2020-02-16 19:34:57 UTC

Reply

PermalinkSo 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 getthat 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.

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

PermalinkSo 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 getthat 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.

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

PermalinkSo 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.

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

www.abelard.org

Andy Walker

2020-02-16 21:00:26 UTC

Reply

PermalinkSo 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.

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

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.

Andy Walker,

Nottingham.

abelard

2020-02-16 23:30:32 UTC

Reply

PermalinkSo 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.

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

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 don't think snowflakery does young people many favours

--

www.abelard.org

www.abelard.org

Pancho

2020-02-16 18:09:22 UTC

Reply

Permalink 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 aobjections 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.

[...]

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.

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.

no argument

but i'd rather that instead of 'infinity' larners were taught to use

some arbitrary large number

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.

So how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

questions has to be a natural number?

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.philosophy rather than of mathematics.

Andy Walker

2020-02-16 19:16:02 UTC

Reply

PermalinkSo how many natural numbers should we tell learners there are.

Is this number also the biggest natural number?

questions has to be a natural number?

Natural number. Perhaps your objection is that I should have used

capital N in Natural?

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].

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.

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.

But that's a question of

philosophy rather than of mathematics.

I don't see why, I thought Cantor nailed it, in mathematics.philosophy rather than of mathematics.

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.

Andy Walker,

Nottingham.

abelard

2020-02-16 17:21:55 UTC

Reply

PermalinkIt is, because I cant think of another occasion when it happened.

Lack of prior art makes something unusual, it does not make something odd,in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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?

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

www.abelard.org

Pancho

2020-02-16 18:07:56 UTC

Reply

PermalinkOn Sun, 16 Feb 2020 14:14:02 +0000, Pancho

Lack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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?

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.

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

PermalinkOn Sun, 16 Feb 2020 14:14:02 +0000, Pancho

It is, because I cant think of another occasion when it happened.

Lack of prior art makes something unusual, it does not make something odd,in many centuries and 1 is an odd number.

even number. If it's neither, then that's even odder.

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?

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.

but i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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?

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.

which does not exist?

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.

--

www.abelard.org

www.abelard.org

Pancho

2020-02-17 00:43:57 UTC

Reply

PermalinkThe 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.

which does not exist?

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

PermalinkThe 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.

which does not exist?

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.

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

www.abelard.org

Keema's Nan

2020-02-17 13:26:49 UTC

Reply

PermalinkOn Mon, 17 Feb 2020 00:43:57 +0000, Pancho

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.

which does not exist?

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.

really just expose their ignorance.

Infinity is undefined, and will remain so until..... er, infinity

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

PermalinkOn Mon, 17 Feb 2020 00:43:57 +0000, Pancho

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.

which does not exist?

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.

really just expose their ignorance.

to show me up. Much better to be corrected here, rather than exposed as

a fool in real life. ;o)

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

PermalinkOn Mon, 17 Feb 2020 00:43:57 +0000, Pancho

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.

which does not exist?

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.

really just expose their ignorance.

to show me up. Much better to be corrected here, rather than exposed as

a fool in real life. ;o)

Infinity is relatively well defined.

In other words, not just - infinity is the quality of being infinite.

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.

Roger

2020-02-16 15:26:25 UTC

Reply

Permalinkbut i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

abelard

2020-02-16 17:27:25 UTC

Reply

Permalinkbut i'd rather that instead of 'infinity' larners were taught to

use some arbitrary large number

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

www.abelard.org

Keema's Nan

2020-02-14 16:08:41 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

Dan S. MacAbre

2020-02-14 16:12:37 UTC

Reply

PermalinkLack of prior art makes something unusual, it does not make something odd,

in many centuries and 1 is an odd number.

Roger

2020-02-14 15:59:33 UTC

Reply

PermalinkPerhaps 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.

Keema's Nan

2020-02-14 16:07:25 UTC

Reply

PermalinkPerhaps 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.

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

PermalinkPerhaps 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.

I am well aware of my previous posts, thanks - and I provided my thicko

reasoning for you to pull to pieces.

Keema's Nan

2020-02-14 16:35:55 UTC

Reply

PermalinkPerhaps 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.

I am well aware of my previous posts, thanks - and I provided my thicko

reasoning for you to pull to pieces.

Keema's Nan

2020-02-15 13:58:30 UTC

Reply

PermalinkPerhaps 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.

I am well aware of my previous posts, thanks - and I provided my thicko

reasoning for you to pull to pieces.

alcohol addiction.

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