If an infinite amount of space had an infinite amount of gas in it, what's the density

I was just wondering this while I was bored :P

No answer. Or rather infinitely many possible answers.

Imagine that space is divided up into cubic meter boxes numbered 1, 2, 3, 4, .... There are obviously an infinite number of those.

I could have a billion gas molecules per box. Then the density would be a billion molecules per cubic meter. But I could also have one molecule per box. Or one molecule every million boxes.

Basically you could have any positive real number at all as the density and still meet the condition of an infinite number of molecules in an infinite number of boxes.

Undefined.

There are different quantities of infinity.

Take a number line for example...
Going one way from zero, there are an infinite number of integers from zero up.
Going both ways from minus infinity to plus infinity there are an infinite number of integers.

While the count on both is "infinity," clearly the second infinity is larger than the first.

Well, that would depend on the unit of the volume. If the unit was anything less than infinity, then the density would probably be either infinite or just undefined.

I am afraid that whilst it sounds reasonable your question does not make sense.
You cannot divide one undefined quantity into another.
I also go on Yahoo! Answers when I'm bored and think about the questions posed.

Infinitely dense.
At the density that is almost the transition from a gas to compressed liquid.