Help me identify this proof

Hi.

A while back i was speaking to a professor of mine. He was telling me about this (trippy) proof some mathematician came up with involving sets and subsets. I dont remember exactly but he said it was something like how he proved that the subset, while being part of the set was actually greater than the set??

An analogy he used was, if you had a ball, you could prove that if you ripped the ball apart into tiny pieces, you could construct two balls of the same size as the original with those pieces.

Don't know if you guys have heard of something like this but I was curious to read about it, problem is i don't know what its called.