Page "Theorem" Paragraph 3

Logically, many theorems are of the form of an indicative conditional: if A, then B.

Such a theorem does not state that B is always true, only that B must be true if A is true.

In this case A is called the hypothesis of the theorem ( note that " hypothesis " here is something very different from a conjecture ) and B the conclusion ( A and B can also be denoted the antecedent and consequent ).

The theorem " If n is an even natural number then n / 2 is a natural number " is a typical example in which the hypothesis is that " n is an even natural number " and the conclusion is that " n / 2 is also a natural number ".