Question

1. a) Prove that the axiom "OSz and 0 3 y implies 0 tion is equivalent to "r 3 y and z 2 0 implies xz ya. ry" in Rudin's presenta- b) Prove that if the above axiom is replaced by "O < x and 0 2y implies 0 ry" in the ordered field axiomatic, it follows that 0, b) 1 <0. How do the rules of signs change? c) Would the above replacement make any difference in the axiomatic of real numbers? If not, indicate an isomorfism between the "standard" and the "new" ordered, complete fields.

Answer 1

270 an 잇나 。

1B) Jy.pl a te de 넛/ 0수1 and 02 2- 2. 2- nie 유tandoldS,wed) ,didos.de