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New page: A '''constructive proof''' demonstrates the existence of a mathematical function, number or object by producing (constructing) it. This is in contrast with other styles of proof, such...
A '''constructive proof''' demonstrates the existence of a [[mathematical]] function, number or object by producing (constructing) it. This is in contrast with other styles of proof, such as proof by contradiction, which asserts the existenc of an object by finding a contradiction if it did not exist.
The [[Axiom of Choice]] assumes the existence of a function without constructing it, and thus all proofs that rely on the [[Axiom of Choice]] are nonconstructive proofs.
The easiest way to prove the existence of [[transcendental]] numbers is by a nonconstructive proof, arguing that the set of [[real number]]s is uncountable while the set of [[algebraic number]]s is countable, and thus transcendental numbers must exist.
[[Category:mathematics]]
The [[Axiom of Choice]] assumes the existence of a function without constructing it, and thus all proofs that rely on the [[Axiom of Choice]] are nonconstructive proofs.
The easiest way to prove the existence of [[transcendental]] numbers is by a nonconstructive proof, arguing that the set of [[real number]]s is uncountable while the set of [[algebraic number]]s is countable, and thus transcendental numbers must exist.
[[Category:mathematics]]