How to read partial ordering in a set?

Question

Let $X$ be a partially ordered set with partial order $\preceq$. Then how can we read $x\preceq y$. Is it $x$ less than or equal l to $y$.?

Answer 1

To be general, I would read $x \preceq y$ as "$x$ precedes $y$." This allows you to talk naturally about partially-ordered sets that are not sets of numbers with the usual $\leq$ order. (For example, you could talk about the set of all people ordered by their ancestral relation.)

The word precedes might also carry less connotation about the order being necessarily a linear/total order, which is a useful feature.