hypothesis
A counter-example.
It's called a proof
The Poincaré Conjecture.
It is a proof.
a proof
A counter-example.
It's called a proof
The Poincaré Conjecture.
It is a proof.
a proof
a proof
Counterexample
it is called a conjecture
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)
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
a conjecture
To be true a Conjecture must be true for all cases.