counterexample
A counterexample is a specific example or case that disproves or contradicts a statement or claim
A counterexample is a specific example or case that disproves or contradicts a statement or claim. In mathematics, it is used to show that a general assertion, theorem, or conjecture is not universally true.
To illustrate this, let’s consider the following statement: “All prime numbers greater than 2 are odd.” This is a commonly known fact, but let’s suppose we want to examine this claim using a counterexample.
If we take the number 8, which is greater than 2 but not a prime number, we can see that it is even. This contradicts the statement that all prime numbers greater than 2 are odd. Therefore, the number 8 serves as a counterexample to disprove the claim.
Counterexamples are a valuable tool in mathematics as they help to identify limitations or exceptions to general statements. By providing a contrary example, they allow mathematicians to better understand the true scope and conditions of a mathematical concept or assertion.
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