Galileo's paradox

proper noun

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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Meanings

proper noun
  1. mathematicsA 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.

Origin

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

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Cite this entry
APA

Galileo's paradox. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Galileo's%20paradox

MLA

“Galileo's paradox.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Galileo's%20paradox. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Galileo's paradox,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Galileo's%20paradox.

Source: Galileo's paradox on Wiktionary, CC BY-SA 4.0.