Cantor's theorem in programming?

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Val-Lee2015-01-02 21:51:08

Programming

Val-Lee, 2015-01-02 21:51:08

Where and how is Cantor's theorem about the uncountability of the segment [0;1] applied in programming??

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3 answer(s)

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Roman Kitaev, 2015-01-02
@deliro

Nowhere. There are no real numbers in programming.

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Mrrl, 2015-01-03
@Mrl

It is used when searching for the root of a function by dividing the segment in half. For any sequence of signs f (x) for the midpoints of the segment, we get a certain number - the root of the equation. Of course, in reality we take only a finite number of steps and get a number from a finite set, but the very fact that the method works and the root exists is based, among other things, on the continuity of the segment. If we had only rational numbers, then the equation x^2=2 would have no root, and we would not have the right to say that we find it with the required accuracy.

A

Armenian Radio, 2015-01-02
@gbg

No way, in programming there are no uncountable sets.