Define a numeric relation that is reflexive, but not symmetric or transitive.

Question

Define a numeric relation that is reflexive, but not symmetric or transitive.

I've googled on this one quite a bit and am stuck.

Answer 1

Here's a somewhat artificial one, but how about: $$ x\sim y \iff y-x = 0 \text{ or } y-x = 1 $$ Note $1\sim 2$ but $2 \not \sim 1$, and $1 \not\sim 3$ even though $1 \sim 2$ and $2 \sim 3$ .