Terminology for all elements of an ordered set $\geq$ a specific element.

Question

This is sort of a silly question, but I don't know whether there is a standard term for the complement of the segment of a well ordered sequence (or more generally, the subset of elements greater than or equal to a chosen element).

I don't like using $O(x)^c$ to refer to the set of elements $\geq x$ since it forces me to use the set as the universe I'm working in, and the notation doesn't seem to be standard.

Answer 1

You could call it the upset ${\uparrow} x$ of $x$, which is pretty standard order theory terminology.