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Questions and Answers
What makes a set countable in mathematics?
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?
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?
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?
What does it mean for a set to be countably infinite?
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What is an alternative term for 'countably infinite' as defined in the text?
What is an alternative term for 'countably infinite' as defined in the text?
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