Re: Contradicrtion-free mathemattics (The new nonstandard analysis

In article <1138586159.061245.241790@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
matthias@xxxxxxxxxxx wrote:

> E. E. Escultura
> >Am still waiting for that contradiction that you claimed to have found in my
> >work
>
> You haven't given nearly enough detail for anyone to find a
> contradiction.* Please:
>
> 1. List your axioms explicitly. Start with a list of the undefined
> notions, then give a formal statement of each of the axioms.
>
> 2. Say exactly what criteria you require to show that something which
> is not an axiom is provable from your axioms.
>
> * Here is an example. You define your real numbers to be the
> completion of a certain initial set. You claim that the sequence
> 1,0.1,0.001, 0.001 does not converge to 0. But in the ordinary sense
> of the word completion that sequence certainly converges to 0. You do
> not define what you mean by ``completion'' and so it is impossible to
> show that you are wrong. But that isn't because you are correct, it is
> only because you have failed to define what you mean by completion. In
> every previous constructive analysis (such as Bishop, Brouwer, etc.,.)
> the sequence above is believed to converge to 0.

Oone would only expect it to converge to 0 if the sequence is
1, 0.1, 0.01, 0.001,...instead of the
1, 0.1, 0.001, 0.001, ... that you posted!
.

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