If the universe is infinitive and there is a precedent of conditions being met, it is impossible for the conditions of life to have not been met somewhere.
If the universe were infinite (and there's no evidence it is) there would be an infinite number of species with a infinite number of members each. But again there's no reason to think the universe is infinite and thus no reason to think that there "must" be aliens.
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Graffiti outside Latin class.
Sed quis custodiet ipsos custodes?
A juvenal prank.
How would one go about proving the universe is infinite? Even if it was Infinite how can we assume that "there will be an infinite number of species with a infinite number of members each"?
Infinity divided by infinity is of meaningless value. If the odds of life forming are infinitesimal, trying to apply it to the infinite size of the universe produces mathematical garbage.
At any rate, there's no reason to believe the universe is infinite anyway.
it is possible to roll a die an infinite number of times and never roll a 6.
same concept.
That something has a probability not equal to 0 doesn't mean it has to happen eventually.
indeed. The fact that there is space does not mean there is life in that space. The argument that there has to be life because there is space is a fallacy.
but just saying the universe is infinite is not enough
it is possible for a universe to be infinite, yet contain only one planet. Infinite is a measure of space, not a description of what is within that space.