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.
Version 2.1.8p2
