Universe is infinté, maybe. But the volume that contains matter is not infinite.
A good approximation is that the universe is about 12-18 (15) billion light years wide, the number of stars is not infinite but a very big number indeed, when calculating you might just as well think of it as infinite.
With all these stars it would be quite stupid to belive that no life exist.
If humans will encounter intelligent life during humanitys life-span is questionable with the distances involved.
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