# Proofs Started by parsonstreet, 12th June 2019 18:21 in Talk & Chat 1. JUN
12
2019

## Proofs

Can you prove that every even number can be divided into two whole numbers?

I ask this because there is potentially an infinite amount of even numbers.  Join BC Forums To Reply 2. JUN
12
2019

## Re: Proofs Can you prove that every even number can be divided into two whole numbers?
Why bother? It's axiomatic. The very definition of an even number requires it to be evenly divisible.

Except zero if you accept that zero is an even number. I suppose you could "divide" it into postive and negative numbers of equal magnitude but that's a bit of a stretch.

 I ask this because there is potentially an infinite amount of even numbers.
There's no 'potentially' about it. You can add 2 to any even number to make a bigger one and repeat the process as many times as you like so the set is definitely infinite.  Join BC Forums To Reply 3. JUN
12
2019

## Re: Proofs

The background question is how can you prove something with infinities or infinite numbers involved.

You can create a random number like

230000000000475867587888378568489000001293847756997879078890
898908908908098908789798767868756564000000000000000000000000
01234566700000000000000000000030000000000000027652

I couldn't even describe this number (name it etc). The fact it has a 2 on the end however implies it can be divided into two whole numbers.

There are number we cannot think about or simply have not thought about in order to asses their properties.

On the other hand there are a huge number of atoms in the known universe which we could I suppose make an estimate of creating a vast sum. There does appear to be vast numbers of discrete objects as yet not calculated but ..still much smaller than infinity.  Join BC Forums To Reply 4. JUN
12
2019

## Re: Proofs

The classic case is the black swan.

Because every swan in Europe was white it became a statement of certainty that being a swan equaled being white.

That was because of lack of access to Australasia. It marked a failure of induction.

But it was compelling.

For some reason 9/111 has been described as a black swan event. But also economic crashes get called this.  Join BC Forums To Reply 5. JUN
12
2019

## Re: Proofs The background question is how can you prove something with infinities or infinite numbers involved.
No it isn't. The question is how can you prove that a given finite number is divisible by two. The fact that there are infinitely many of such numbers is a red herring. Each of the numbers in the infinite set is subject to the same treatment and if that set consists only of even numbers, then each member of the set is by definition so divisible.

 You can create a random number like [big number removed because it messed up the text wrapping. Even-ness of number stipulated] I couldn't even describe this number (name it etc). The fact it has a 2 on the end however implies it can be divided into two whole numbers.
It's not implied, it's an incontravertible fact.

 There are number we cannot think about or simply have not thought about in order to asses their properties.
Nevertheless you have asked a question specifically about numbers with a specified common property. The fact that there are infinitely many of them doesn't alter the fact that each of them shares the property specified with any or all of the others.

 On the other hand there are a huge number of atoms in the known universe which we could I suppose make an estimate of creating a vast sum.
How is this relevant?

 There does appear to be vast numbers of discrete objects as yet not calculated but ..still much smaller than infinity.
"Much smaller than infinity" is a tautology. Anything that is finite is infinitely smaller than infinity. Your problem here is you want infinity itself to be somehow included in your examination of individual members of an infinite set. It's unnecessary. I'll give you another example:

There are infinitely many prime numbers. And yes I can prove that by disproving the counterproposition that the set of all primes is finite, but the point is it makes no difference how big the set is if I want to prove that all primes are divisible only by themslves and one. 7 is prime because it satisfies the definition. 83 is prime for the same reason. They would be prime whether the set of all primes is finite or infinite, it doesn't matter. And it likewise doesn't matter that the set of even numbers contains infinitely many members... each of them satisfies the definition otherwise they wouldn't be in the set.  Join BC Forums To Reply 6. JUN
12
2019

## Re: Proofs Nevertheless you have asked a question specifically about numbers with a specified common property. The fact that there are infinitely many of them doesn't alter the fact that each of them shares the property specified with any or all of the others.

The problem is that numbers are human constructions and symbols. So if we have not created a symbol for a number how can we analyse it? It seems that infinity is simply unimaginable.

Bertrand Russell tried to convert mathematics to logic but considered that he failed in the end.  Join BC Forums To Reply 7. JUN
12
2019

## Re: Proofs Can you prove
You've PROVEN time and time again that you don't even know what proof is.

It isn't worth my effort answering this qeustion for this reason.

(Scrotum will now childishly attention seek by claiming this means I can't answer it, he will be ignored).  Join BC Forums To Reply 8. JUN
12
2019

## Re: Proofs I couldn't even describe this number (name it etc).
That's because you're thick.

HTH  Join BC Forums To Reply 9. JUN
12
2019

## Re: Proofs That's because you're thick. HTH
Abuse.  Join BC Forums To Reply 10. JUN
12
2019

## Re: Proofs The problem is that numbers are human constructions and symbols.
No they are not. Numbers and the symbols that represent them are not the same things.

 So if we have not created a symbol for a number how can we analyse it?
Do you think a computer manipulates symbols? It doesn't. Neither do we, we just use them to keep track of what we're actually doing, which is manipulating numbers.

 It seems that infinity is simply unimaginable.
Even numbers, which is what I thought this was about, are easy to imagine. You've somehow convinced yourself that you can't analyse any of them unless you consider all of them at once.

 Bertrand Russell tried to convert mathematics to logic but considered that he failed in the end.
A failure which has nothing whatever to do with the simple arithmetic axiom you supposedly wanted to discuss.  Join BC Forums To Reply + Reply to Thread + Post New Thread
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