Date: Mon, 02 Oct 2006 09:06:49 -0500 (CDT)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-02-FALL@uni.edu
Subject: [810-080-02-FALL] Is it EVEN or is it ODD - two cases...

Hi 080 students,

    To prove something for any integer that involves it ending
up EVEN or ODD, you need to prove two different cases.

    Since all integers are either EVEN or ODD, if you prove
it for both cases, you then know it is proven for ALL INTEGERS.

    n is even would be case #1

    n is odd would be case #2.

    Do you recall that the definition of even means

         that for case #1, n = 2a for some integer a????   I hope so!

    Similarly, for case #2, n = 2a + 1 (or 2b + 1)
                                           since n is ODD.

    Mark