[Cementjungle]

"So in an infinite universe, there must be other occurrences of life."

That is exactly correct, but only if you believe that we (life) came to be as a result of random events.

In fact, if we did indeed come to be by chance, then in an infinite universe there would necessarily be infinite instances of life.

[Pelham]

"In fact, if we did indeed come to be by chance, then in an infinite universe there would necessarily be infinite instances of life."

Olber's Paradox, the "dark night sky paradox", argues against an infinite universe.