sets questions


It has been many years since I worked with sets, so my questions are
probably going
to sound silly...Sorry about that.

If I have a set of, say natural numbers...it can automatically be
assumed, by definition,
that a subset of that of my original set are still natural numbers.

To continue, is there some kind of operation that I can use to create
a subset?

Say I wanted only the odd natural numbers. So far the only think I
can think of
is to create a set of odd natural numbers and do the intersection with
the original set.
But if I can create the new set by hand, there is no point.

I hope my questions is clear enough. Basically I want to filter
elements of a set to create
a new, subset, of the same type.

Thanks,
-Mike

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