As usual, Emma_Acid is correct. A line that starts at point A and goes off to infinity is just as long as a line that never starts nor stops.

Similarly, there are the same number of positive integer multiples of 5 (i.e. {0, 5, 10, 15, 20, ...}) as there are integers (i.e. {... -3, -2, -1, 0, 1, 2, 3, ...} ), or even rationals (i.e. {x/y} where both x and y are integers).

There are, however, more real numbers than rational numbers (the first is `uncountably infinite', the second is `countably infinite').

ShaunZero, on 27 October 2009 - 04:06 PM, said:

I've always wondered about these scientific ideas. If we can't measure infinite, and therefore can not logically point to any instance of it, how can we say that those things(Black Holes energy, etc) are infinite?

We say black holes are infinite because that is what the mathematics suggest (a black hole is basically `dividing by zero'). However infinities are usually avoided in science. It is one thing to say that something is

*unbounded* - i.e. as you accelerate something towards the speed of light its mass increases continually - but that isn't the same as being infinite. If you had infinite energy you could accelerate something to infinite mass; but of course you don't have infinite energy in the first place.

The fact that a black hole is theoretically an infinity (usually referred to as a `singularity') is unsatisfactory to many scientists. A common believe is that once we've figured out how to merge general relativity and quantum mechanics together, this infinity will disappear.

As a corollary, classical electrodynamics predicts an electron (or proton) has an infinite charge density - but this infinity was removed by quantum mechanics.