Eric - yes, \\(1/x\\) doesn't preserve any of those three things. But the puzzle asked for a function from \\(\mathbb{R}\\) to \\(\mathbb{R}\\), and \\(1/x\\) isn't that. It's a function from \\(\mathbb{R}- \\{0\\} \\) to \\(\mathbb{R}- \\{0\\}\\).

On the other hand, \\(1/x\\) is nice because it preserves _multiplication!_

**Puzzle:** find a function from \\(\mathbb{R}\\) to \\(\mathbb{R}\\) that doesn't preserve the order, metric or addition, but preserves multiplication.

On the other hand, \\(1/x\\) is nice because it preserves _multiplication!_

**Puzzle:** find a function from \\(\mathbb{R}\\) to \\(\mathbb{R}\\) that doesn't preserve the order, metric or addition, but preserves multiplication.