With all the stars in the universe, why isn't the sky saturated with light? [duplicate]

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?

• This is actually an old exercise, have a look at en.wikipedia.org/wiki/Olbers%27_paradox – AtmosphericPrisonEscape Jul 16 '18 at 11:59
• @drone6502 - your question is exactly what is known as Olbers' paradox. Look it up. – Florin Andrei Jul 16 '18 at 19:38
• +1 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 1:30

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.