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Countable Sets in Mathematics
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Countable Sets in Mathematics

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Questions and Answers

What makes a set countable in mathematics?

  • It can be made in one to one correspondence with the set of real numbers
  • It can be made in one to one correspondence with the set of natural numbers (correct)
  • It has a finite number of elements
  • It has an equal number of elements as the set of natural numbers

    • What is an injective function with respect to countable sets?

  • It maps each element in the set to a finite number of elements
  • It maps each element in the set to a unique real number
  • It maps each element in the set to an infinite number of elements
  • It maps each element in the set to a unique natural number (correct)

    • Who proved the existence of uncountable sets?

  • Leonhard Euler
  • Georg Cantor (correct)
  • Euclid
  • Isaac Newton

    • What does it mean for a set to be countably infinite?

    <p>It is countable and has an infinite number of elements</p> Signup and view all the answers

    What is an alternative term for 'countably infinite' as defined in the text?

    <p>At most countable</p> Signup and view all the answers

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