"Galileo's paradox" meaning in English

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  "etymology_text": "Named after the scientist Galileo, though he did not originate the concept.",
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          "name": "Paradoxes",
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      "glosses": [
        "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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          "set theory",
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          "demonstration",
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          "infinite",
          "infinite"
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          "set",
          "set"
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          "positive",
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          "integer",
          "integer"
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          "square",
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          "square root",
          "square root"
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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."
      ],
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        "mathematics",
        "sciences",
        "set-theory"
      ],
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        "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."
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