Nice! It's fun to think about infinite sets, too.

**Puzzle.** If \$$A\$$ and \$$B\$$ are possibly infinite sets, and there's an injection \$$f: A \to B\$$ and an injection \$$g: B \to A\$$, is there a bijection between \$$A\$$ and \$$B\$$?

**Puzzle.** If \$$A\$$ and \$$B\$$ are possibly infinite sets, and there's a surjection \$$f: A \to B\$$ and an surjection \$$g: B \to A\$$, is there a bijection between \$$A\$$ and \$$B\$$?