> But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero.
No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity.
> since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.
It never goes to infinity either. Zero and infinity are the limits.
> An infinite number of small numbers adds up to infinity.
Well, no. It depends. For instance the sum of 1/n goes to infinity, but not the sum of 1/n². And since the luminosity of a star decreases with the square of the distance, I incline to believe the sum does converge.
But again, that would require some serious, albeit probably not very hard maths. I've never seen anyone discuss this. Instead everyone seems to immediately assume the sum would diverge. That's not obvious at all.
An infinite number of small numbers does not always add up to infinity! Since the apparent brightness of a star is an inverse-square law, if you assume there are an infinite number of stars, each 1 light year further away from you in a line and all the same brightness, you end up with that area being only 64%[1] brighter than it would seem with only the first star. Seems like a pretty simple resolution to this paradox to me.
The part that grandparent is overlooking is that while luminosity decreases as to the square of the distance, the number of stars in a given angular diameter of space increases as to the square of the distance. The two effects cancel each other out and so Olbers Paradox can't be resolved by that method.
No, it never goes to zero, it just gets fainter. An infinite number of small numbers adds up to infinity.
> since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
As the article mentions, the sky is black because we cannot see infinity. We can only see the observable universe.