In an ordered field, S, with positive elements, P, for all x,y elements of S define x<y if y-x is an element of P,

prove that only one of the following can be true:

x<y,x=y,y<x

Also prove that if x,y,z are arbitrary and x<y and y<z then x<z.

- Sep 15th 2009, 07:41 PMamm345Transitivity and Ordered Fields. How do you prove this? Please help.
In an ordered field, S, with positive elements, P, for all x,y elements of S define x<y if y-x is an element of P,

prove that only one of the following can be true:

x<y,x=y,y<x

Also prove that if x,y,z are arbitrary and x<y and y<z then x<z. - Sep 15th 2009, 08:11 PMNonCommAlg
- Sep 15th 2009, 08:14 PMamm345
To define a total order S.

- Sep 15th 2009, 08:19 PMThePerfectHacker