BY PICTORIAL REASONING state why infinity a a infinity a

BY PICTORIAL REASONING, state why infinity + a = a + infinity = a for all a (other than infinity). In fact, it is true for all a, but the parenthetical phrase is harder to see. (That is, this item shows that infinity is the identity for this operation of addition.) EXTRA CREDIT. By pictorial reasoning, state why infinity + infinity= infinity.

Solution

(P) Adding to a number makes it larger.

Infinite cardinal \"numbers\" violate this, because when one adds to an infinite set (without taking anything away), the resulting set may not be larger than the original set. (I.e., when A, B are disjoint and A is infinite, ABAB may not be larger than A.)