Space is dark. But if we direct telescopes to seemingly dark portions of sky, we see that it is filled with galaxies. If the universe is theoretically infinite, wouldn't an infinite number of photons be reaching the earth and illuminating the night sky brighter than it appears?
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Logic1: If the universe is infinite AND static, the sky will be saturated with light.
Note "AND."
Logic2: If the sky is not saturated with light, the universe is not infinite or not static.
Note "OR."
Logic1 = Logic2
Observation: the sky is not saturated with light. Therefore: the universe is not infinite or not static.
We know that the universe is dynamic, at least.

Kornpob Bhirombhakdi
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This is a good question and a reasonable one. There's no reason to penalize the OP by down voting it. @FlorinAndrei since someone had already left a comment linking to an article about the paradox 7 hours earlier, your comment "Look it up" is redundant, and in my opinion, not at all helpful. – uhoh Jul 19 '18 at 01:30