Generalized term for minimal/maximal, least/greatest element? Is there a generalized term for a minimal/maximal element and/or a least/greatest element of a set, respectively, anlong the lines of bounds for lower/upper bounds or extrema for the minimal/maximal values of a function?
The question arises as it is very tedious to always write "A maximal/minimal element (often abbreviated as "maximum/minimum") of a set is ... not to be confused with a least/greatest element of a set ..." instead of "An extremum of a set is ..." or "A bound of a set is ...".
Alternatively, one could just use one of the two expressions  and state in the beginning that both are meant. However, I feel that a generalized term would not only be more elegant but also more practical.
So to conclude: Are you aware of any such a term? If not, what would be your suggestion to formulating text that are concerned with max/min and least/greatest? Maybe further, what are the conventions you use?
Edit: To clarify, I am aware that minimal/maximal elements, least/greatest elements and upper/lower bounds are in general not equal. I am asking for two seperate terms, one used to generalize minimal and maximal elements and one to generalize least and greatest elements. The mentioning of extrema of functions, bounds and inf/sup are just examples to give an idea of what such a generalization would look like.
 A: Those two sets of words actually do not always equate depending on context:
There are many situations that could possibly involve order theory, duality, total order, partial order, frontiers just to name a few. The word references can differ between multiple subjects like analysis and concepts even inside set theory itself.  You have to be specific as to what context and objects to which you are referring otherwise it is a bit of fudged layman speak at which point you can call it whatever you like because it becomes debased from that exact context.  This is a situation where brevity can attack you given an astute audience at the risk of sounding aloof at the worst. At the best this probably introduces unclear or not so well defined documents.  This is perhaps seen as anti-thesis to  pure mathematics.
As an example:
"In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum).."
Yet:
"In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists. Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used.
The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is the least element in T that is greater than or equal to all elements of S, if such an element exists. Consequently, the supremum is also referred to as the least upper bound (or LUB)."
Or even futher different:
"It looks like m should be a greatest element or maximum but in fact it is not necessarily the case: the definition of maximal element is somewhat weaker. Suppose we find s E S with max S <= s, then, by the definition of greatest element, s <= max S so that s = max S. In other words, a maximum, if it exists, is the (unique) maximal element."
"The converse is not true: there can be maximal elements despite there being no maximum. Example 3 is an instance of existence of many maximal elements and no maximum. The reason is, again, that in general <= is only a partial order on S. If m is a maximal element and s E S, it remains the possibility that neither s <= m nor m <= s."
References:
https://en.wikipedia.org/wiki/Maximal_element
https://en.wikipedia.org/wiki/Infimum_and_supremum
