non-constructive proof

The uniform boundedness principle yields a simple non-constructive proof of this fact.

This also applies to non-constructive proofs, using a refined A-translation.

They are particularly used for non-constructive proofs.

In addition, some adherents of these schools reject non-constructive proofs, such as a proof by contradiction.

This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play.

Taken together, the letters of December 2 and 7 provide a non-constructive proof of the existence of transcendental numbers.

The above proof is an example of a non-constructive proof disallowed by intuitionists:

This theorem can be proven via a constructive proof, or via a non-constructive proof.

Dov Jarden gave a simple non-constructive proof that there exist two irrational numbers a and b, such that a is rational.

The non-constructive proof starts by assuming that the set of real numbers is countable, or equivalently: the real numbers can be written as a sequence.

Some non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true (proof by contradiction).

(It turns out that is irrational because of the Gelfond-Schneider theorem, but this fact is irrelevant to the correctness of the non-constructive proof.)

Dov Jarden's non-constructive proof, also attributed to Peter Rogosinski and Roger Hindley, proceeds as follows:

Kreisel worked in various areas of logic, and especially in proof theory, where he is known for his so-called "unwinding" program, whose aim was to extract constructive content from superficially non-constructive proofs.

This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem) which proves the existence of a particular kind of object without providing an example.

Typically, supporters of this view deny that pure existence can be usefully characterized as "existence" at all: accordingly, a non-constructive proof is instead seen as "refuting the impossibility" of a mathematical object's existence, a strictly weaker statement.

The non-constructive proof does not construct an example a and b; it merely gives a number of possibilities (in this case, two mutually exclusive possibilities) and shows that one of them-but does not show which one-must yield the desired example.

For finite games, and games where the appropriate instance of Markov's rule can be constructively established by means of bar induction, then the non-constructive proof of a winning strategy for the first player can be converted into a winning strategy.