real numbers usual order element join irreducible none completely join irreducible '''join prime''' math x leq vee b math implies math x leq text x leq b math generalized obtain notion '''completely join prime''' dual notion '''meet prime''' every join prime element also join irreducible every meet prime element also meet irreducible converse holds math l math distributive let math l math bottom element element math x math math l math atom math x math exists element
Formal science Mathematics Pure mathematics Algebra Lattice theory