Consider the set S ={1000,999,...,0,...,999,1000}.

Suppose that we consider S with alphabetical order.

(a) Is this a total order on S?

(b) Is 8 a lower bound on the set of negative integers in S?

(c)Is 10 a lower bound on the set of negative integers in S?

(d) Does the set S have a minimum in this order?

(e) Is 1 an upper bound on the negative integers in S?

(f) Does the set of negative integers in S have a maximum in this order?

(g) Show that addition does not respect alphabetical order.