Can a lattice be formed with just a single element? Because for a single element, both Greatest Lower Bound and Least Upper bound exists and is equal to the same element. So can this element be called as a lattice?
2026-04-02 23:17:33.1775171853
Is a single element a Lattice?
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Yes, for every kind of algebra, in the sense of Universal Algebra, i.e., a set endowed with a set of finitely operations, there is a one element algebra, which can be achieved by taking the quotient of that algebra by the universal congruence relation, which is the relation $A^2$ on the algebra with base set $A$.
Lattices are also algebras is this sense. (See, for example, here.)
Considering lattices only as ordered structures, we still have one-element lattices, by the exact reason you mentioned.
So, yes, you are right.