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A counterexample is an example (usually of a number) that disproves a statement. When seeking to prove or disprove something, if a counter example is found then the statement is not true over all cases. Here's a basic and rather trivial example. I could say "There is no number greater than one million". Then you could say, "No! Take 1000001 for example". Because that one number is greater than one million my statement is false, and in that case 1000001 serves as a counterexample. In any situation, an example of why something fails is called a counterexample.
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Can a theorem have a counterexample?
No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
What is an example for which a conjecture is incorrect?
A counterexample.
What is a case in which a conjecture is not true?
Counterexample
What is a counterexample?
a number wich disproves a proposition For example, theprime number 2 is a counterexample to the statement "All prime numbers are odd."
What a counterexample?
a number wich disproves a proposition For example, theprime number 2 is a counterexample to the statement "All prime numbers are odd."
Does every statement have a counterexample?
No. Not if it is a true statement. Identities and tautologies cannot have a counterexample.
Can a theorem have a counterexample?
No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
What is the counterexample for 16?
-16
What is an example for which a conjecture is incorrect?
A counterexample.
What is a case in which a conjecture is not true?
Counterexample
What is a counterexample?
a number wich disproves a proposition For example, theprime number 2 is a counterexample to the statement "All prime numbers are odd."
What a counterexample?
a number wich disproves a proposition For example, theprime number 2 is a counterexample to the statement "All prime numbers are odd."
What is an example of a counterexample in geometry?
IF TX then Plano
What is a antonym for example?
non-example, counterexample,
What is an example of a counterexample for the difference of two whole numbers is a whole number?
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
Is a counterexample of all planets have moons?
Yes, the planet Mercury does not have any moons. This serves as a counterexample to the statement "all planets have moons."
A counterexample is sufficient to prove that a conjecture is false?
Yes.
