Quentin Anciaux kirjoitti:
 > 2009/6/3 Torgny Tholerus <tor...@dsv.su.se>:
...
 >> 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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