What's matter?

Imagine you take a sheet of paper and cut it exactly in half. Now, you take the two pieces and cut them in half again. And you do this again and again.

If you had magic scissors, (that were) very, very small and sharp, do you think you could continue cutting the pieces in half forever?

Or, instead, would you reach a moment when you found a "little piece" so small that it was completely impossible to divide anymore?