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# What is the set of odd numbers less than 14?

In the ordinary sense, yes. In the sense of set theory, no. –

Bernard

May 27 '17 at 23:1

Infinite sets behave differently than finite sets. Consider the map f:N→O where O is the set of all odd numbers. This can be written as a bijection f(n)=2n−1 and they have the same cardinality (|N|=|O|) –

Dando18

May 27 '17 at 23:2

Also a question to think about: if two sets are infinite, than how is one larger than the other? What constitutes their size? This is why we look at the density and countability of sets. –

Dando18

May 27 '17 at 23:2

Take the integers and the even integers (since they are a group and subgroup whereas the odds are not). If you defined "larger" to mean index bigger tha, then Z would be larger, [Z:2Z]=2, but in terms of cardinality both sets are the same size. They can be put in 1-1 correspondence with each other. –

sharding4

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Q: What is the set of odd numbers less than 14?