Math CentralQuandaries & Queries


Question from Islam, a student:

How can I prove that the set of all odd natural numbers is an infinite set. Thank you.


This depends on what you want to assume (or your course has said) about infinite sets. Two possible ways to go:

  1. 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.

  2. 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!


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS