Skyler
Puritan Board Graduate
Jonathan,
You are right that radiation received falls off with the square of distance, but with an infinite number of stars you would still get radiation from every point in the sky. Occultation by dark objects would not be sufficient as any radiation absorbed by such objects would necessarily have to be re-radiated by that object at some point due to conservation of energy.
This is true, but because the universe is composed of discrete units, and radiation sources are not mathematical points, "every point in the sky" still constitutes a finite set of radiation sources (albeit a large one).
For a simple analogy, consider a pixellated circle. From the center of the circle, you can draw a ray in any direction, but it will always intersect with one of a finite number of pixels.