Let P D .X; / be a lattice and let m be an element of the lattice. Prove that m is maximum in P if and only if 8x 2 X; x _ m D m if and only if 8x 2 X; x ^ m D x. What is the analogous statement for a minimum element?

Lecture 4: Recall: a trace is the intersection of the surface with one of the coordinate planes x=k, y=k and z=k. Traces will be used to graph quadratic surfaces in 3-dimensional space. How to graph in 3-D. Step 1: Identify the general traces x=k g=k, z=k and select one family that is easy to draw....