COUNTEREXAMPLE Meaning and
Definition
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A counterexample is a specific case or example that disproves a general statement or claim. It is used in mathematics, logic, science, and other fields to challenge or negate a proposed theory, hypothesis, or conjecture. By providing a counterexample, one can demonstrate that a statement or idea is incorrect or invalid.
In mathematics, a counterexample is typically a specific set of values or an instance where a particular equation, theorem, or principle fails to hold true. For example, consider the statement "All prime numbers are odd." A counterexample to this statement would be the number 2, which is a prime number but is also an exception to the general rule that primes are odd. Therefore, by providing a counterexample, we can disprove the claim that all prime numbers are odd.
In logic and reasoning, counterexamples are used to challenge the validity of a logical argument or the truthfulness of a general proposition. By presenting a counterexample, one can demonstrate that the argument or proposition does not always hold true and may have exceptions.
Overall, a counterexample is a powerful tool for identifying the limits, exceptions, or flaws in a given statement, theory, or argument. It provides concrete evidence to contradict an assertion and helps promote critical thinking and a deeper understanding of concepts.
Common Misspellings for COUNTEREXAMPLE
Etymology of COUNTEREXAMPLE
The word "counterexample" derives from the combination of two words: "counter" and "example".
The term "counter" comes from the Old French word "contre", meaning "opposite" or "against". It entered English through Middle English and Latin roots.
On the other hand, "example" has Latin roots from the word "exemplum", meaning "sample" or "model". It became commonly used in both French and English.
When combined, "counter" in this context implies something that contradicts or opposes, while "example" refers to a specific case or instance. Therefore, a "counterexample" can be understood as an example that contradicts or disproves a particular statement, theory, or generalization.
Similar spelling words for COUNTEREXAMPLE
- counterinsurgency,
- counterclaim,
- counterfeiter,
- counterespionage,
- countercheck,
- countertenor,
- countercurrent,
- counterpunch,
- counter tube,
- counterpoise,
- counterplay,
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- counterchallenge,
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- counterstrike,
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- contretemps,
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- counterpoint,
- counterargument,
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- counterpart,
- counter check,
- counterbore,
- countermelody,
- countermeasure,
- counter-drill,
- counterpoison,
- countercoup,
- counterculture,
- countercharge,
- counterpoised,
- counterfire,
- countermove,
- counteractive.
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