I have only seen the notation $f : A \rightarrow B$ used for discussing functions. Can this notation be used for relations that are not functions?
For example, $\tan : \mathbb R \rightarrow \mathbb R$ appears to define a relation that is not left-total (for example $\frac \pi 2\in \mathbb R$ is not mapped to anything in codomain $\mathbb R$) and hence not a function. Would it be incorrect to express this relation, that is not a function, using this notation?
Edit: To borrow a great example from Arthur's answer below, consider the notation $\le\; : \mathbb R \rightarrow \mathbb R$. This seems to me to unambiguously express a relation that, while left-total is certainly not functional (e.g. $(3, 3), (3, 4) \in \;\le$) and hence not a function. If it's unambiguous, surely this notation can be used to express this relation that is not a function...
I guess I could express my question more clearly as: is there anything in the expression $f:A\rightarrow B$ that asserts that $f$ is not merely a relation but specifically a function?