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- In mathematics, a counterexample is:
- A specific example that disproves a general statement or hypothesis1.
- An example that meets the mathematical statement's condition but does not lead to the statement's conclusion2.
- Used to prove the boundaries of possible theorems and modify conjectures to produce provable theorems3.
- Important for logic and provides the foundation for almost all mathematics4.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.A counterexample is a specific example or instance that disproves a general statement or hypothesis. More formally, a counterexample is an example that demonstrates the falsity of a proposition or conjecture. In mathematics, a counterexample is typically used to disprove a conjecture or to show that a theorem is false in some cases.clubztutoring.com/ed-resources/math/counterexam…A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion.www.cuemath.com/data/counterexample/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.en.wikipedia.org/wiki/CounterexampleA 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.www.storyofmathematics.com/counterexample/ - People also ask
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