# counterexample

[ˌkaʊntərɪɡˈzɑːmp(ə)l]

## counterexample Definition

• 1an example that opposes or contradicts a hypothesis or theory
• 2an example used to disprove a statement or prove the opposite of a given proposition

## Using counterexample: Examples

Take a moment to familiarize yourself with how "counterexample" can be used in various situations through the following examples!

• Example

The mathematician provided a counterexample to the conjecture.

• Example

The scientist used a counterexample to disprove the theory.

• Example

A counterexample is a powerful tool in logic and mathematics.

## Phrases with counterexample

• ### counterexamplemethod

a technique used in mathematics and logic to prove the validity of a statement by showing that its negation leads to a contradiction

Example

The counterexample method is often used in proving theorems in mathematics.

• ### existenceofcounterexamples

the fact that a counterexample exists to a statement or hypothesis, indicating that it is false

Example

The existence of counterexamples is crucial in disproving conjectures in mathematics.

• ### counterexampleproperty

a property of a mathematical object or system that can be disproved by finding a counterexample

Example

The counterexample property of a function is important in determining its domain and range.

## Origins of counterexample

from 'counter-' meaning 'against' + 'example'

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## Summary: counterexample in Brief

'Counterexample' [ˌkaʊntərɪɡˈzɑːmp(ə)l] refers to an example that opposes or contradicts a hypothesis or theory. It is a powerful tool in logic and mathematics, used to disprove statements or prove the opposite of a given proposition. The 'counterexample method' is a technique used in mathematics and logic to prove the validity of a statement by showing that its negation leads to a contradiction.

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