Definition
Contradiction
A contradiction happens when statements cannot all be true at the same time.
What it means
Follow the facts until they clash. If the reasoning says the same thing must be true and not true, the starting claims cannot all be right. That clash is a contradiction.
Remember it
Think of two arrows reaching opposite signs at once: “true” and “not true.” Stop and check the assumptions.
Example
Suppose a whole number is both even and odd. “Even” means divisible by 2, while “odd” means not divisible by 2. Those two claims cannot both hold, so the assumption creates a contradiction.
Watch for
Two people giving different answers is not automatically a contradiction. Their claims must be unable to be true together.
Common mix-up
A counterexample shows that a general claim is false. A contradiction shows that a group of claims cannot all be true together.
Exact meaning
A contradiction is a conflict in which a set of statements, assumptions, or consequences cannot all be true together—often because they lead to both a claim and its negation.