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| Math Central | Quandaries & Queries |
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Question from Islam, a student: How can I prove that the set of all odd natural numbers is an infinite set. Thank you. |
Islam,
This depends on what you want to assume (or your course has said) about infinite sets. Two possible ways to go:
- Bijection: If you can use the fact that the property of being infinite is preserved by 1-1 correspondence, and you know that the natural numbers are an infinite set, construct that 1-1 correspondence.
- By contradiction: finite sets have largest elements. Assume P to be that element and find a (whoops!) bigger one. Guess it wasn't finite after all.
Good Hunting!
RD
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