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Countable Sets in Mathematics

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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

Countable Sets in Mathematics

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Questions and Answers

What makes a set countable in mathematics?

What is an injective function with respect to countable sets?

Who proved the existence of uncountable sets?

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

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

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