| slovo | definícia |
existence proof
(foldoc) | non-constructive proof
existence proof
(Or "existence proof") A proof that something exists
that does not provide an example of that thing or a method for
finding an example. (A constructive proof does provide such an
example or method).
For example, for any pair of finite real numbers n < 0 and p > 0
there exists a real number 0 < k < 1 such that
f(k) = (1-k)*n + k*p = 0.
A non-constructive proof might proceed by observing that as k
changes continuously from 0 to 1, f(k) changes continuously from n
to p and, since they lie either side of zero, f(k) must pass
through zero for some intermediate value of k. This proof does
not tell us what that value of k is, only that it exists.
Cantor's proof that the real numbers are uncountable can be
thought of as a non-constructive proof that irrational numbers
exist. There are existence theorems with no known constructive
proof.
(2014-08-23)
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