Does Olber's paradox claim that in an infinite universe (both in space and in time) light should be able to reach you from any direction?
Consider the thought experiment of placing an infinite number of light-emmiting points on the interval [0, 1] on all the rational points.
In this case, the space is bounded, the number of stars is infinite but it would still be mostly dark (this is the well known mathematical fact that there many many many more irrational numbers than there are rational numbers)
Now if we transpose this idea to space.. I think we could easily have an unbounded space, homogeneous, with infinite number of stars but still it would be mostly black...
Sure, I can relax the condition that stars should be placed on rational grid points in the space.. And I also think one could get away with stars as balls and not points...
Or can't I?
Is there a mathematical proof of why this is a legitimate paradox?
It feels wrong to me.. But again.. My intuition is a random machine