Re: Turing completeness of the functional paradigm?

Mr Elliot wrote:
> To get rational and real numbers from Peano's axioms you have to add set
> theory.

I see (but I thought they were merely Peano sequences of Peano
sequences, i.e. vectors of this or other sort, as is every mathematical
object).

> The integers are infinitely countable.
> Goodstein's theorem, which can be stated within Peano's axioms,
> can be proved with set theory but cannot be proved with Peano's axioms.
> It's a true statement about integers that can't be proved with Peano's
> axioms. Thus Peano's axioms are incomplete.

I surrender to your argument, Mr Elliot.

Thank you very much for writing.

Tom

.

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