Define S~={E(xn):(xn)S}, with +~,a~ and ~. Prove that (S~,+~,~,~) is an ordered field. Note 1. We can regard qQ as q={q,q,q,}S so that EqS~. Note 2. Under the definition of (S~,+~,~,~) we can define the absolutely value in the similar manner