For another example, the equation from Example 3.28 (page 109) is best phrased as a conditional statement, to make clear the assumption that is an integer.
Theorem If is a non-negative integer, then . A theorem of the form “If , then ,” can be regarded as a device that produces new information from . Whenever we are dealing with a situation in which is true, then the theorem guarantees that, in addition, is true. Since this kind of expansion of information is useful, theorems of the form “If P, then Q,” are very common.