Quentin Anciaux kirjoitti:
> 2009/6/3 Torgny Tholerus <torgny.domain.name.hidden>:
...
>> How do you know that there is no biggest number?
>
> You just did.
> You shown that by assuming there is one it entails a contradiction.
>
>> Have you examined all
>> the natural numbers?
>
> No, that's what demonstration is all about.
>
Clearly you two disagree on what {0, 1, 2, 3, ...} means.
All definitions of natural numbers I have seen imply that N+1 is a
natural number whenever N is. Then there clearly is no biggest number.
But I can see someone could have philosophical objections to the
conventional definition. I've heard of ultrafinitists, e.g., but have
not checked how they define natural numbers (if they do).
jp
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Received on Wed Jun 03 2009 - 16:07:09 PDT