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!
--------------
All your questions are answered in my responses to matthias@xxxxxxxxxxx of Feb. 1.
E. E. Escultura
.
Relevant Pages
- Re: Contradicrtion-free mathemattics (The new nonstandard analysis
... >>Am still waiting for that contradiction that you claimed to have found in my ... List your axioms explicitly. ... > of the word completion that sequence certainly converges to 0. ...
(sci.math) - Re: Contradicrtion-free mathemattics (The new nonstandard analysis
... >Am still waiting for that contradiction that you claimed to have found in my work ... List your axioms explicitly. ... of the word completion that sequence certainly converges to 0. ...
(sci.math) - Re: The state-of-the-art in mathematics
... Because I believe you will contradict one of your claims in this particular proof, show me, and everyone else, wrong and reply with a wellfounded proof by contradiction. ... >the axioms must well-define the given mathematical space. ... >the given mathematical space and well-defined by the axioms. ... >irrational is ill-defined or nonsense unless there is some algorithm ...
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(sci.math) |
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