Re: Cantorian pseudomathematics

Han de Bruijn 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?

Good thing you have quantifier dyslexia, hence you'll never figure it
out.

Jiri

.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... Virgil wrote: ... 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. ... So if we have a sensor that measures x within a distance delta from a, ... then fwill be measured as within a distance eps from f. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... Continuity means the following: a function fis continuous in a iff ... So if we have a sensor that measures x within a distance delta from a, ... then fwill be measured as within a distance eps from f. ... Since the definition requires that this be so for EVERY epsilon greater ...
    (sci.math)
  • Re: Cantor Confusion
    ... Han de Bruijn wrote: ... Consider that the number of balls as a function of time has infinitely ... problem is that you mathematicians do not understand what continuity IS. ...
    (sci.math)
  • Re: lim eps->0 int(eps,1) x^x dx
    ... Helmut Richter wrote: ... > Han de Bruijn: ... Yes, the integral exists, but neither continuity nor existence of a ... no matter how you define f. ...
    (sci.math)
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