Re: infinity ...


albst...@xxxxxx wrote:
> My argumentation is very easy:
> Every nat. number represents a set. If you look at the first 100 nat.
> numbers, the 100th nat. number "100" represents the set {1, ... , 100}.
> As this holds for every nat. number, if there are infinite nat. numbers
> there must be a infiniteth nat. number representing this set.

No, there musn't. There is no logical basis on which to draw
this conclusion from your premise.

> But the definition of the nat. numbers with complete induction leads to
> the consequence, that there could not be an infinite nat. number.

Correct. Your first "conclusion" is merely an assertion, not
based on axioms. The only rule you're using is "there must",
the same thing Tony Orlow does: shout loudly when you don't
have a mathematical basis for "must".

There "must" based on WHAT? WHY must there?

- Randy

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