Some reasons to teach lattice theory to undergraduates

First-year students in mathematics and computer science are often troubled with the Schröder-Bernstein theorem, which proves that the natural ordering between cardinal numbers is in fact a partial order, but has a lengthy and convoluted proof. A more accurate study of order structures (often neglected by basic course) would, however, allow to see this fact as an almost immediate consequence of a much simpler, and very powerful, theorem due to Bronislaw Knaster and Alfred Tarski. Continue reading