Galileo's paradox
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(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.
Galileo's paradox
In his writings on mathematics, Galileo's paradox highlights how the set of perfect squares and the set of all positive integers can be put into a one-to-one correspondence despite the former seeming smaller.
In his writings on mathematics, Galileo's paradox highlights how the set of perfect squares and the set of all positive integers can be put into a one-to-one correspondence despite the former seeming smaller.
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