hypothesis
The Poincaré Conjecture.
a proof
It is a proof.
Counterexample
hypothesis
The Poincaré Conjecture.
A counter example is a statement that shows conjecture is false.
pie tree
a proof
a proof
It is a proof.
It's a counterexample.
Counter example
Counterexample
It's called a proof
a conjecture is disproved if it is shown to be false. this can be done by providing a single concrete example (e.g. with actual numbers, functions, etc) that shows the conjecture's premise does not necessarily lead to its conclusion. alternatively, a conjecture could be shown to be false (i.e. disproved) by demonstrating that IF it were true then a logical consequence would be a clearly wrong statement (e.g. 2 + 2 =5)