on wikipedia I read that a lattice is describable both as order-relation and as algebraic structure.
First I must say I have more to do with informatics but I am interested in the mathematical basics of informatics or even in mathematical logic in general.
I find it hard formulating my question, please be a little forgiving with me.
About lattices, I don't understand what it "means" or why it is of importance and interest that there is "to two elements a and b each a supremum and an infimum", that there are, defined as algebraic structure, two inner binary, commutative and associative operations. Then there obviously is an importance of the absorbtion and idempotency laws to the idea of lattices and at last the special meaning of the fact that a "algebraic structure" statement about a lattice is translatable into an "order-relation" one to begin with.
I don't understand why a lattice is the foundation for the proof of the existence of a smallest fixpoint.
What I would like to understand is what is "the special thing" about lattices. On an intuitive level.