What's the difference between "function" and "relation" in logic? What's the difference between "function" and "relation" in logic?
Why do we cosider them apart?
I think every relation expresses a function...

In FOL (first-order logic) a function symbol has terms (i.e. "names") as input and output.
For every pair $n,m$ of natural numbers, $+(n,m)$ (usually writteh: $n+m$) denotes a number.
Predicate (or relation) symbols have terms as input and produce sentences.
For every pair $n,m$ of natural numbers, $<(n,m)$ (usually writteh: $n < m$) is true or false according to the fact that the number $n$ is less or not than the number $m$.
