Why are "join" and "meet" named as they are? In the context of partially ordered sets, why are the words for supremum and infimum "join" and "meet"? I find the nomenclature puzzling, especially since the English words "join" and "meet" are synonyms, but denote opposite concepts when talking about posets.

Does anyone know how these concepts got these names?

(Cross-posted on HSM)
"Join" and "meet" for partially ordered sets could be based on elementary set theory, where you have the union ($\cup$) or intersection ($\cap$) of two or more sets; join $(\vee)$ and meet $(\wedge)$ are their analogues for posets.
"Join" and "meet" for partially ordered sets could be based on elementary set theory, where you have the union ($\cup$) or intersection ($\cap$) of two or more sets; join $(\vee)$ and meet $(\wedge)$ are their analogues for posets.