Let be two Dedekind cuts. Is it true that ? where , the meaning of is similar.
I met with this problem while trying to prove the equivalence of two formulations of addition of real numbers, therefore, to avoid iterative proof please restrict addition to rationals only. Thanks!
Thanks but the definition of Dedekind cut prevents this from being part of a Dedekind cut, since the left part of a dedekind cut should not have greatest element. I am using Karel Hrbacek's "Introduction to Set Theory"(P88 Def5.4) and Baby Rudin(P17 (III)).