My question is exactly like in the title: What is the difference between unary relations and one-element relations?
If I start with definitions, given a set $X$ unary relation $\theta$ is a subset of $X$ (while n-ary relation would be a subset of $X^n$ of course). So for every $a \in X$, we would have $a \in \theta$.
Then, a one-element relation $\phi$ would be what? Is it a subset of $X^n$, but relating only one element with itself?
I couldn´t find any sources for this.
It would help to see some examples of such relations, let´s say on a set of natural numbers $\mathbb{N}$. Thanks a lot.