indirect proof | 3.3: Indirect Proofs - Mathematics LibreTexts

Keyword	CPC	PCC	Volume	Score	Length of keyword
indirect proof	1.09	0.2	7765	50	14
indirect	0.38	0.6	3796	53	8
proof	1.53	0.7	9219	71	5

Keyword	CPC	PCC	Volume	Score
indirect proof	0.54	0.9	6683	32

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3.3: Indirect Proofs - Mathematics LibreTexts
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https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/03%3A_Proof_Techniques/3.03%3A_Indirect_Proofs

WebWe can use indirect proofs to prove an implication. There are two kinds of indirect proofs: proof by contrapositive and proof by contradiction. In a proof by contrapositive, we actually use a direct proof to prove the contrapositive of the original implication.

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3.3: Indirect Proofs- Contradiction and Contraposition
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https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/03%3A_Proof_Techniques_I/3.03%3A_Indirect_Proofs-_Contradiction_and_Contraposition

WebA Pythagorean triple is a set of three natural numbers, a a, b b and c c, such that a2 +b2 = c2 a 2 + b 2 = c 2. Prove that, in a Pythagorean triple, at least one of a a and b b is even. Use either a proof by contradiction or a proof by contraposition.

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How to do an Indirect Proof | 3 Easy Steps & Examples (Video)
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https://tutors.com/lesson/indirect-proof-definition-examples

WebJan 11, 2023 · Indirect proof in geometry. Suppose we state this: Given ∠A and ∠B are supplementary angles: Prove \angle B<180° ∠B < 180°. This is easily proved by indirect proof: Assume \angle B\ge 180° ∠B ≥ 180° the opposite of our original position. \angle A+\angle B=180° ∠A + ∠B = 180° definition of supplementary angles.

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Indirect Proofs - Stanford University
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https://web.stanford.edu/class/archive/cs/cs103/cs103.1152/lectures/02/Small02.pdf

WebWriting a Disproof The easiest way to disprove a statement is to write a proof of the opposite of that statement. The opposite of a statement X is called the negation of statement X. A typical disproof is structured as follows: Start by stating that you're going to disprove some statement X. Write out the negation of statement X. Write a normal proof that …

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2.6 Indirect Proof - Whitman College
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https://www.whitman.edu/mathematics/higher_math_online/section02.06.html

WebThere are two methods of indirect proof: proof of the contrapositive and proof by contradiction. They are closely related, even interchangeable in some circumstances, though proof by contradiction is more powerful. What unites them is that they both start by assuming the denial of the conclusion.

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Proof by Contradiction | Brilliant Math & Science Wiki
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https://brilliant.org/wiki/contradiction/

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. It's a principle that is reminiscent of the philosophy of a certain fictional detective:

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Indirect Proofs - Stanford University
stanford.edu

https://web.stanford.edu/class/archive/cs/cs103/cs103.1198/lectures/02-IndirectProof/Indirect%20Proofs.pdf

WebProof: By contrapositive; we prove that if n is odd, then n2 is odd. Let n be an arbitrary odd integer. Since n is odd, there is some integer k such that n = 2k + 1. Squaring both sides of this equality and simplifying gives the following: n2 = (2k + 1)2 n2 = 4k2 + 4k + 1 n2 = 2(2k2 + 2k) + 1. From this, we see that there is an integer m

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CS103 Cynthia Lee Winter 2019 Keith Schwarz Guide to …
stanford.edu

https://web.stanford.edu/class/archive/cs/cs103/cs103.1194/handouts/Guide%20to%20Indirect%20Proofs.pdf

WebGuide to Indirect Proofs. Keith Schwarz. This handout explores issues specific to the two types of indirect proofs we've explored so far (proofs by contradiction and contrapositive), some common techniques that arise when working with them, and some recurring pitfalls to avoid. Proof by Contrapositive.

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4.3: Indirect Proof - Engineering LibreTexts
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https://eng.libretexts.org/Under_Construction/Book%3A_Discrete_Structures/04%3A_Mathematical_Induction_and_Proofs/4.3%3A_Indirect_Proof

WebBook: Discrete Structures. 4: Mathematical Induction and Proofs. 4.3: Indirect Proof. Expand/collapse global location. 4.3: Indirect Proof. Page ID. Table of contents. 3.5.3 Indirect Proof. Science works to either prove or disprove assertions. This is contrary to those who insist that science seeks only to disprove assertions.

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Indirect Proof Explained (Contradiction Vs Contrapositive)
calcworkshop.com

https://calcworkshop.com/proofs/indirect-proof/

WebJan 17, 2021 · Indirect Proof Definition. An indirect proof doesn’t require us to prove the conclusion to be true. Instead, it suffices to show that all the alternatives are false. There are two forms of an indirect proof. Proof By Contraposition; Proof By …

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