Re: infinity

"Gordon Collins" <poster02@xxxxxxxxxxx> writes:

> But then we would not need the axiom of
> induction. The acceptance of that axiom is an acceptance that we
> cannot complete an infinite sequence of operations.

Just what is it we cannot do? After all, we cannot literally count
up to n, if we choose n large enough. You remark that

> An infinite sequence of operations
> cannot be completed, even mathematically.

but it's easy as pie to "complete an infinite sequence of operations"
mathematically. We just say, for example, "let omega be the sequence
of numbers obtainable from 0 by iterating the operation of adding
one" and then go on to add one to omega.


.

Relevant Pages

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  • Re: Raatikainens critique of Chaitin
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