Galileo's paradox
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.
Proper noun
Galileo's paradox
- 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.
Origin of Galileo's paradox
Named after the scientist Galileo, though he did not originate the concept.
Questions about Galileo's paradox
- What does Galileo's paradox mean?
- Galileo's paradox means 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.
- What part of speech is Galileo's paradox?
- Galileo's paradox is a proper noun.
Words near Galileo's paradox in the dictionary
Source and license
Adapted from Wiktionary: Galileo's paradox (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
Last updated:
Cite this entry: “Galileo's paradox.” Word.ws, https://word.ws/galileo%27s_paradox. Based on Wiktionary, CC BY-SA 4.0.