An infinite set which cannot be put in one-to-one correspondence with the set of natural numbers. For example, the set of real numbers between zero and one is non-denumerable, and contains more numbers than all the integers, or even all the rational numbers, both of which are denumerable.

How do you prove something is Denumerable?

By identifying each fraction p/q with the ordered pair (p,q) in ℤ×ℤ we see that the set of fractions is denumerable. By identifying each rational number with the fraction in reduced form that represents it, we see that ℚ is denumerable. Definition: A countable set is a set which is either finite or denumerable.

What is the meaning of Denumerable sets?

A set is denumerable if it can be put into a one-to-one correspondence with the natural numbers. You can't prove anything with a correspondence that doesn't work.