An integer, c, is called the immediate predecessor of an integer a
if c < a and there does not exist an integer b such that c < b < a. The
number x is called the smallest element of a set, A, if x is in A and
for all a in A, x < a or x=a. Suppose our set A is
N x N={(m,n)|m,n are natural numbers}.
- Define (x,y) < (z,w) if and only if
(x < z) or (x=z and y < w).
(Also known as the dictionary order.) What elements have immediate
predecessors? Does the set have a smallest element?
- Define (x,y) < (z,w) if and only if
(x-y < z-w) or (x-y=z-w and y < w).
What elements have immediate predecessors? Does the set have a
smallest element?
Due Friday, Dec. 4th at Noon.