Ordered sets may (or may not) have last elements. Is there a common way of denoting the last element of an ordered set. For example if we define $A$ to be the ordered set $\langle \mathbb N, >\rangle$ (the naturals in reverse order), $A$ has a last element $0$. (...,3,2,1,0).
Would it make sense to denote $A$'s last element $a_{\omega^{\downarrow}}$ ($\omega^{\downarrow}$ being the order type of $A$) or maybe $a_{|A|}$?
or something better?