Thread: least upper bound property

Having just started a course in analysis,I am confused about the reals having this least upper bound property in their order . Because suppose we consider the set of all odd integers which is a subset of the reals..how can I say that the least upper bound of this subset is in the reals?Infact how can I say that this subset is bounded above?

The set of odd integers has neither upper bound nor least upper bound. One of the axioms of real numbers says that nonempty sets that have an upper bound also have a least upper bound. The premise of this axiom is false for odd integers, so the axiom says nothing about this set.

I see.. thanks.