week6

This week we still learned something about proofs.  Sometimes if the origin statement is hard to prove, we can disprove it. Sometimes we need to break down the statement. For example, ‘the floor of x is the largest integer <or= x’, we need to show the floor of x is integer, it is the largest and it is <= x. sometimes we need to prove by cases. For instance, ‘for any positive integer n, n^2 + n is even’, so we need to consider the cases where n is odd and where n is even. Proving is abstract and needs every step is reasonable.