We are always going to get into trouble when we continue to scatter around terms and phrases like "absolute", "infinity", and "division by zero". As dear old Korzybski said, "The map is not the territory". Just because a word exists, it does not follow that it reflects an underlying reality. Remember the word "cloudcuckooland"?

We would not, I hope, argue that because pink elephants are alleged to exist in Cloudcuckooland, that they must have existed on Earth, and are therefore extinct. So why do we talk about "division by infinity"? - a process just as ridiculous - except, of course, as part of one of our wonderful mathematical abstractions. "Part of" - of course, not. It

* is *nothing but a mathematical abstraction. Since there is no such real number as infinity (hence we get more rubbish like the 'infinity plus one' arguments) just think of, say, a 50 digit prime number. Now, using long division, divide that into one. Bet you wish you hadn't started!

Density = mass / volume. If it has mass, especially large mass, it will have a real volume, so dividing by that will not give us infinite density. Repeat the above exercise, except divide your 50 digit prime number by a very small number with no common factors, and beginning with 27 noughts. When you have completed both exercises (or given up) you will understand why mathematics was blessed with unreal quantities such as infinity - both infinitely large and infinitely small. Are there any cases in experimental science when you are likely to need the number 0.000000000000000000000000000000000000000000000000000735962715377391362543227772854321? Even the number following the zeros is likely to be way beyond the accuracy limitations of any experiment.

So "

How does General Relativity predict zero volume/infinite density of Black holes?".

Well, if it does, it shouldn't. What it really means is very, very high. Or, if you want to be more precise, say "probably greater than 1 x 1 0^77". Inventing words like infinity is just a lazy way of describing *seemingly* boundless quantities.

Cat