Can You Keep Infinitely Compressing Until A File Is 1 Byte?

When a colleague of mine first ran across the original PKARC program (this was a while ago) he thought it was the greatest thing. He figured that he could reduce each of his files to a single byte by re-running PKARC on a.ARC file enough times.

I couldn't convince him otherwise because, lacking a detailed knowledge of software compression techniques, I had only my own gut instinct to rely on. That and the fact that, if he were correct, it would mean that the number of different possible files was limited to.