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1. Dictionary

   counterexample

   /ˈkaʊntərɪɡˌzɑːmp(ə)l/

   noun

   • 1. an example that opposes or contradicts an idea or theory: "the media presented him as a counterexample to the common stereotypes"

   Scrabble Points: 27

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2. www.storyofmathematics.com › counterexampleCounterexample – Explanation and Examples - The Story of ...

   www.storyofmathematics.com › counterexample

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   A counterexample is a specific case that proves a statement false. Learn how to identify and write counterexamples for conditional statements, and see examples from math and logic.

3. www.merriam-webster.com › dictionary › counterexampleCounterexample Definition & Meaning - Merriam-Webster

   www.merriam-webster.com › dictionary › counterexample

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   The meaning of COUNTEREXAMPLE is an example that refutes or disproves a proposition or theory.

4. Videos

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     Counterexample in Mathematics | Definition, Proofs & Examples

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     Counterexample

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     What is a Counterexample? (and why philosophers use fictional examples)

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5. en.wikipedia.org › wiki › CounterexampleCounterexample - Wikipedia

   en.wikipedia.org › wiki › Counterexample

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   A counterexample is an exception to a generalization that disproves it in logic, mathematics and philosophy. Learn how to find and use counterexamples to test conjectures, prove theorems and refute arguments.

6. simplicable.com › en › counterexample11 Examples of a Counterexample - Simplicable

   simplicable.com › en › counterexample

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   Nov 14, 2023 · A counterexample is a specific example that contradicts a general statement or hypothesis. This is used to disprove statements in logic, rational thought and debate. As such, counterexamples are stronger than nonexamples that are more often used to illustrate a concept. The following are illustrative examples of a counterexample.

7. k12.libretexts.org › Bookshelves › Mathematics2.6: Conjectures and Counterexamples - K12 LibreTexts

   k12.libretexts.org › Bookshelves › Mathematics

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   Nov 28, 2020 · counterexample: A counterexample is an example that disproves a conjecture. fraction: A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

8. www.skillfulreasoning.com › basic_concepts › counterexamplesFinding Counterexamples - skillfulreasoning.com

   www.skillfulreasoning.com › basic_concepts › counterexamples

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   A counterexample to a supposedly necessary condition is an example showing that the condition isn’t really necessary after all. Likewise, a counterexample to a putatively sufficient condition (or set of jointly sufficient conditions) is an example showing that the condition (or set) isn’t really sufficient after all.

9. People also ask

   What is an example of a counterexample?

   • A counterexample is a specific example for which a statement is untrue. The existence counterexample proves the statement is false, even if it is often, mostly, or almost entirely true. Counterexamples are incredibly important for logic, which is, in turn, important because it provides the foundation for almost all mathematics. This section covers:

   Counterexample – Explanation and Examples - The Story of Mathematics

   www.storyofmathematics.com/counterexample/

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   What is a counterexample method?

   • The "counterexample method" is a powerful way of exposing what is wrong with an argument that is invalid. If we want to proceed methodically, there are two steps: 1) Isolate the argument form; 2) Construct an argument with the same form that is obviously invalid. This is the counterexample. Let's take an example of a bad argument.

   How to Prove an Argument Invalid by a Counterexample - ThoughtCo

   www.thoughtco.com/prove-argument-invalid-by-counterexample-2670410

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   What is a counterexample to a supposedly necessary condition?

   • A counterexample to a supposedly necessary condition is an example showing that the condition isn’t really necessary after all. Likewise, a counterexample to a putatively sufficient condition (or set of jointly sufficient conditions) is an example showing that the condition (or set) isn’t really sufficient after all.

   Finding Counterexamples

   www.skillfulreasoning.com/basic_concepts/counterexamples.html

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   What is a counterexample in logic?

   • 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.

   Counterexample – Explanation and Examples - The Story of Mathematics

   www.storyofmathematics.com/counterexample/

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   How do you write a counterexample?

   • For example, one could change a statement so that it doesn’t apply to all real numbers but just to positive numbers. Writing a counterexample requires finding a specific case when a statement is wrong and showing how the case disproves the statement. When showing that a statement is false, it is necessary to use a specific example.

   Counterexample – Explanation and Examples - The Story of Mathematics

   www.storyofmathematics.com/counterexample/

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   What is a counterexample in mathematics?

   • In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers can then avoid going down blind alleys and learn to modify conjectures to produce provable theorems.

   Counterexample - Wikipedia

   en.wikipedia.org/wiki/Counterexample

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10. www.thoughtco.com › prove-argument-invalid-byHow to Prove an Argument Invalid by a Counterexample - ThoughtCo

    www.thoughtco.com › prove-argument-invalid-by

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    Nov 19, 2019 · The "counterexample method" is a powerful way of exposing what is wrong with an argument that is invalid. If we want to proceed methodically, there are two steps: 1) Isolate the argument form; 2) Construct an argument with the same form that is obviously invalid. This is the counterexample. Let's take an example of a bad argument.