Re: infinity

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > b implies a, but knowing that a number is finite is not the same as ever being
> > able to pin it down. You cannot pin down the largest finite natural, but can
> > you deny that, if in concept it existed, that it would be, without a doubt,
> > finite? This is precisely the same situation with this sum.
>
> Just as an even prime number greater than 2 would be even.
> Discussing the properties of non-existent numbers seems
> rather pointless.
>
> Why are you so worried about the non-existent largest finite?
> It does not exist. You even agree to that every so often.
> The fact that it does not exist means that it is not finite.
> Nor is it infinite. Just as all those even prime numbers
> greater than 2 are not even, because they do not exist.
> Who cares that if they did exist, they would have to be
> even. If they did exist, there would be some serious
> contradictions in our definitions of 'prime' and 'even'
> and calling them 'even', or any number 'even', would
> be meaningless. If such a contradiction existed you
> would be able to prove that every number was both even
> and not even.
>
> Stephen
>
When you look at a set of consecutive whole numbers starting from 1, if you
know the set size, you know the last element, and if you know the last element
you know the set size. However, for the set as a whole, you claim the set isze
is infinite, and all elements are finite, which is a contradiction. For any
range of values, finite or infinite, the largest element and the set size are
the same.
--
Smiles,

Tony
.

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