Roachboy:
finite - Definition from the Merriam-Webster Online Dictionary
infinite - Definition from the Merriam-Webster Online Dictionary
Merriam Webster defines the infinite as the boundless, or endless. I think that's the most standard generic definition.
There are different ones depending on the field in which you delve. Religion, mathematics, etc. have slightly different variations.
So to answer your (possibly rhetorical but whatever) question: endless and infinite seem to be the same, and you don't necessarily have to exhaust all of them since it is mathematically possible to prove that something is infinite. (A universally accepted notion)