Galileo's paradox

English

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

Galileo's paradox

(set theory) 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.

单词	Galileo's paradox
释义	Galileo's paradox English Etymology Named after the scientist Galileo, though he did not originate the concept. Proper noun Galileo's paradox (set theory) 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.
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