Re: Cantorian pseudomathematics

In article <9fa5$43f451a0$82a1e228$17908@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Virgil wrote:

Asking whether any physically derived function is continuous at any
point you have yourself just proved to be impossible to answer, so that
continuity of functions is NEVER observable, and therefore must be
outlawed by HdB's anti-mathematicism.

Continuity means the following: a function f(x) is continuous in a iff

lim f(x) = f(a)
x->a

This is materialized into: |x - a| < delta ==> |f(x) - f(a)| < eps

So if we have a sensor that measures x within a distance delta from a ,
then f(x) will be measured as within a distance eps from f(a) . Delta
and eps are the uncertainities. What is "NEVER observable" about this?

Since the definition requires that this be so for EVERY epsilon greater
than zero, it cannot be observed for epsilons too small to be observed.


The best one could possibly say is that some measured functional
relation has no DETECTABLE discontinuities, which is quite a bit short
of saying that it does not have any at all.
.

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  • Re: Cantorian pseudomathematics
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    (sci.math)