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- A counterexample is an exception to a proposed general rule or law12345. It is a specific instance for which a given statement is false35. In formal logic, a statement is “false” if it is not true in every single circumstance3. Even if it is usually true or sometimes true, it is false. For this reason, finding even one case where the statement is false makes it false3.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.
In logic (especially in its applications to mathematics and philosophy ), a counterexample is an exception to a proposed general rule or law, and often appears as an example which disproves a universal statement.
en.wikipedia.org/wiki/Counterexamplecounterexample noun coun·ter·ex·am·ple ˈkau̇n-tər-ig-ˌzam-pəl : an example that refutes or disproves a proposition or theorywww.merriam-webster.com/dictionary/counterexam…A counterexample is a specific instance for which a given statement is false. In formal logic, a statement is “false” if it is not true in every single circumstance. Even if it is usually true or sometimes true, it is false. For this reason, finding even one case where the statement is false makes it false.www.storyofmathematics.com/counterexample/counterexample [ koun-ter-ig-zam-p uhl, -zahm- ] show ipa noun an example that refutes an assertion or claim.www.dictionary.com/browse/counterexampleAn example that disproves a statement (shows that it is false). Example: the statement "all dogs are hairy" can be proved false by finding just one hairless dog (the counterexample) like below.
www.mathsisfun.com/definitions/counterexample.ht… WebThe meaning of COUNTEREXAMPLE is an example that refutes or disproves a proposition or theory.
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A counterexample is any exception to a generalization. In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are lazy."
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WebCounterexample definition: an example that refutes an assertion or claim.. See examples of COUNTEREXAMPLE used in a sentence.
WebCounterexample Definition. A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. Counterexample Math. Instead of showing that …
WebA counterexample is a specific instance for which a given statement is false. In formal logic, a statement is “false” if it is not true in every single circumstance. Even if it is …
WebCheck pronunciation: counterexample. Definition of counterexample noun in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, …
WebCounterexample. An example that disproves a statement (shows that it is false). Example: the statement "all dogs are hairy" can be proved false by finding just one hairless dog (the counterexample) like below.
Web6 days ago · counterexample. Other forms: counterexamples. Definitions of counterexample. noun. refutation by example. see more.
Webnoun. An example that refutes or disproves a hypothesis, proposition, or theorem. American Heritage. An example used to support an argument or claim that is in …
Web2 days ago · an example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary. Copyright © HarperCollins …
Counterexamples | Lesson (article) | Lessons | Khan Academy
WebA counterexample to a mathematical statement is an example that satisfies the statement's condition(s) but does not lead to the statement's conclusion. Identifying …
Counterexample -- from Wolfram MathWorld
Web4 days ago · A counterexample is a form of counter proof. Given a hypothesis stating that F (x) is true for all x in S, show that there exists a b in S such that F (b) is false, …
COUNTEREXAMPLE definition in American English | Collins …
Web5 days ago · noun. an example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary. Copyright © HarperCollins …
COUNTEREXAMPLE Definition & Usage Examples | Dictionary.com
WebCounterexample definition: . See examples of COUNTEREXAMPLE used in a sentence.
Counterexample in Mathematics | Definition, Proofs & Examples
WebNov 21, 2023 · A counter example is an example that refutes or disproves a proposition or theory. A counterexample can be something very simple in real life. There are many …
counterexample - Wiktionary, the free dictionary
WebJan 29, 2024 · ( logic) An example that counters a general rule; an exception to a general rule; a specific instance of the falsity of (and falsifiability of) any proposed …
2.6: Conjectures and Counterexamples - K12 LibreTexts
WebNov 28, 2020 · Definition; conjecture: A conjecture is an educated guess that is based on examples in a pattern. counterexample: A counterexample is an example that …
Counter-example - definition of Counter-example by The Free …
Weban example or fact that is inconsistent with a hypothesis and may be used in argument against it. Collins English Dictionary – Complete and Unabridged, 12th …
Counterexample: Definitions and Examples - Club Z! Tutoring
WebA counterexample is a specific example that disproves a general statement. It is a powerful tool in mathematics and other fields where statements are made about general …
6.7: Proof by counterexample - Mathematics LibreTexts
WebDefinition: Counterexample. Example \ (\PageIndex {1}\) Sometimes we want to prove that \ (P \not\Rightarrow Q\text {;}\) i.e. that \ (P \rightarrow Q\) is not a tautology. Recall. The …
Counter-examples - FutureLearn
WebDefinition: A counter-example to an argument is a situation which shows that the argument can have true premises and a false conclusion. ... If finding a counter …
counter-example noun - Oxford English Dictionary
WebFactsheet. What does the noun counter-example mean? There is one meaning in OED's entry for the noun counter-example. See ‘Meaning & use’ for definition, usage, and …
Counter Definition & Meaning - Merriam-Webster
Web1. : a piece (as of metal or plastic) used in reckoning or in games. 2. : something of value in bargaining : asset. 3. : a level surface (such as a table, shelf or display case) over …
Web1 day ago · 5. A counter-example in the non-metabelian case 13 References 14 1. Introduction The regularity of geodesics (i.e., isometric embeddings of intervals) is one of …
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