Little Bits of Time

A random thought I had the other day: if you cut time down into smaller and smaller sections (second > millisecond > microsecond etc.) could you be able to cut it down to an infinitely small size, or would their would be a point where it was impossible to cut down anymore and you're left with a sort of "time atom"? And if you were, could the time atom be split like a regular atom? I know the answer is almost certainly no, but hey, it's fun to imagine.