Join and meet processes or procedures.
I guess the words make ome kind of sense , but it is not obvious. The word supremum is equally dis enchanting as is infinitum.
Any collection of things naturally has an extent when one looks for one. This extent , if it is mental is dependent on whether it is visually apprehended or by some other means. If by some other means, sequence takes primary position in the process, if visual then some Metron takes primary position. The meet and join process is to find what begins and ends a sequence or visually what starts the Metron measurement and what ends it.

Clearly this determination becomes more complex as the kind of collection is determined. Sometimes it is a meaningless process.
If I know the boundary of the collection I can make some stab at what is contiguous to it. However the meet is so specific , that it fails most of the time except in the lineal/ sequential cases. cases.
the definition is arcane. What it means is that some ordering process is imposed on a collection. The ordering is confusingly called <, which is usually a quantitative process of ordering. Ordering does not have to be quantitative, it can be customary like the alphabet.
I think I prefer the "alpha and the omega"


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