All finite sets are recursively enumerable (they are also decideable, a stronger property). Many countably infinite sets are also recursively enumerable, though not all are. Sets with a cardinality greater than that of the natural numbers (such as the set of real numbers) are not recursively enumerable.

What is difference between enumerable and Denumerable?

is that enumerable is capable of being enumerated; countable while denumerable is (mathematics) capable of being assigned numbers from the natural numbers especially applied to sets where finite sets and sets that have a one-to-one mapping to the natural numbers are called denumerable.

How do you know if a set is finite or infinite?

The set having a starting and ending point is a finite set, but if it does not have a starting or ending point, it is an infinite set. If the set has a limited number of elements, then it is finite whereas if it has an unlimited number of elements, it is infinite.