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There are many kinds of statement that are not theorems:

A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be.

A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication.

A statement can be false.

A statement can be self-contradictory for example, "This statement is false".

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