Theoretically, could you just keep cutting something in half

forever?

You could not, because you will not last forever to do so. What tedious work that would be... The very first time you succeeded you'd be doubling your workload, and it would just multiply from there. Such a thing would drive the most theoretical person sane.

Aren't theories wonderful things? In theory someone could do this, the same as, in theory, when you place enough monkeys before typewriters you'll either get the complete works of Shakespeare or a typical posting record for a chatroom addict.

You can only cut something in half once... after that, you're quartering it... or cutting something else in half. So theoretically, the only way to cut something in half forever is to take forever to do it.

Zeno's Paradox. It can be paraphrased about like this. Suppose I wish to cross a distance. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance . . . and so on forever. The consequence is that I can never get to the other side of the room.

Robert Anton Wilson used another of Zeno's paradox in Quantum Psycology to show the flaw of pure logic. The theory is logically sound, but ultimately wrong. Likewise, you could theoretically continue to cut something in half indefinately, but really there is a smallest unit that can be divided. If you enjoy this sort of thinking I recomend Wilson's books, especially Quantum Psychology, it's a fun read.

our known science only has a few sub-atomic particles that can be measured, but of course there has to be sub <-> atomic particles, since according to natural law there is no such thing as absolute nothing. but cafe's post is the most correct as far as practical reasoning goes.

mmm, thanks for the good answers, guys :)

It should be possible, but whether or not it is remains to be seen. In theory, it is impossible to divide something until it ceases to exist... conservation of mass states that matter can never be truly "destroyed." If you blow up a table and manage to find each and every little piece, capture all the smoke from the burning, etc, you'll have exactly as much mass as you started with. In practice though, as of now anyway, there is a point where you can no longer chop something in two, because we presently lack the technology to take a subatomic particle apart. You can go down to a hydregen atom sans electron, but no farther.