Siteadmin, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators
125,789
edits
Changes
Jump to navigation
Jump to search
mLine 1:
Line 1: − +
Reverted edits by Googly (Talk); changed back to last version by Foxtrot
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 existence of an object by finding a contradiction if it did not exist. Such a proof is called '''nonconstructive'''.
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 existence of an object by finding a contradiction if it did not exist. Such a proof is called '''nonconstructive''' and is not valued as highly by mathematicians, especially in [[applied mathematics]] and [[computer science]].
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 [[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.