³1username³2JoshuaGrosse³2name³2text_default³2version³21³2ts³2980496605³2ip³2129.97.130.42³2data³2newauthor³31³3minor³31³3text³3A lattice is a set L, together with two binary operations v,^, such that for any a,b,c in L, 

    ava=a                   a^a=a                   (idempotency laws)
    avb=bva                 a^b=b^a                 (commutativity laws)
    av(bvc)=(avb)vc         a^(b^c)=(a^b)^c         (associativity laws)
    av(a^b)=a               a^(bvc)=a               (absorption laws)

If avb=b, or equivalently a^b=a, we say that a<=b. Thus defined, <= forms a PartialOrder on L, and moreover (L,v,^) is the unique lattice associated therewith. TotalOrderedSet''s'' and BooleanAlgebra''e'' are two important types of lattice. 
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