# Math Help - Order Relations, immediate sucessors and predecessors

1. ## Order Relations, immediate sucessors and predecessors

We have an order relation of Z+ x Z+ (where Z+ denotes the positive integers.)
(a,b) < (c,d) if either a - b < c -d or a -b = c - and b < d
is an order relation

(a) which elements have immediate predecessors?
(b) which elements have immediate successors?
(c) Does the set Z+ x Z+ have a smallest element?

Can someone help I am really lost of this one.

2. either a - b < c -d or a -b = c - and b < d
Something unclear about "= c -". Is it supposed to be "= c - d" or is "-" just a syntactic long dash?

In general, I would take a graph paper and draw some arrow from smaller points to greater. I need some intuition to figure this out.