What is the connection element between meet of a subset and join of a poset?

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In a preordered set or partially ordered set then the meet or infimum of a subset of elements is, if it exists, the largest element which is smaller or equal to all the elements in the set

If $x$ and $y$ are elements of a poset, then their join, or supremum, is an element $x \vee y $ of the poset such that...

I would like to know the element in common that can 'connect' a meet of a subset with a join of a poset