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Proof by contradiction - Wikipedia
WEBIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction.
En.wikipedia.org3.3: Proof by Contradiction - Mathematics LibreTexts
WEBApr 17, 2022 · The basic idea for a proof by contradiction of a proposition is to assume the proposition is false and show that this leads to a contradiction. We can then conclude that the proposition cannot be false, and hence, must be true.
Math.libretexts.orgProof by Contradiction - Math is Fun
WEBIn a proof by contradiction, the contrary (opposite) is assumed to be true at the start of the proof. After logical reasoning at each step, the assumption is shown not to be true. Example: Prove that you can't always win at chess. Let us start with the contrary: you can always win at chess.
Mathsisfun.comProof by Contradiction | Brilliant Math & Science Wiki
WEBproof by contradiction (also known as indirect proof or the method of reductio ad absurdum) is a common proof technique that is based on a very simple principle: something that leads to a contradiction can not be true, and if so, the opposite must be true.
Brilliant.orgProof by Contradiction - Gordon College
WEBTo prove a statement P is true, we begin by assuming P false and show that this leads to a contradiction; something that always false. Many of the statements we prove have the form P ) Q which, when negated, has the form P ) Q. Often proof by contradiction has the form.
Math-cs.gordon.edu2.4: Proof by Contradiction - Mathematics LibreTexts
WEBOct 18, 2021 · The “proof by contradiction” rule allows us to turn an explanation of this type into an official proof. If we assume that a particular assertion is true and show that this leads to something impossible (namely, a contradiction), then we have proven that our assumption is wrong; the assumption must be false, so its negation must be true:
Math.libretexts.orgProof by Contradiction and Contrapositive - nordstrommath.com
WEB3.4 proof by contradiction and Contrapositive. 🔗. In this section we will learn two new proof techniques, contradiction and contrapositive. Both proof techniques rely on being able to negate mathematical statements. 🔗.
Nordstrommath.com