Galileo's paradox

Etymology
Named after the scientist Galileo, though he did not originate the concept.

Proper noun

 * 1)  A demonstration of a surprising property of infinite sets. Some positive integers are squares while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares; yet for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other.