First, second, third, thirtieth, two ninety first, a millionth, hundred billionth. Infineth is the a word to express the position of infinite in a countable series of things.
Plato: How many attempts does humanity have to crack the puzzle of life?
Einstein: I don't think that's countable.
Bhakta: True. But, when someone solves it, I think it'll seem like the infineth attempt to us.