Ohda: Definition of Order in Baby Rudin

[Bacle2]

Hi, All:

Just curious:

Rudin defines order in his "Baby Rudin" book ; an order relation < in a set S, as a relation* satisfying, for any x,y,z on S:

1) Either x<y , y<x , or y=x

2)If x<y and y<z , then x<z , i.e., transitivity.

Just curious: why is Rudin only considering only total orders in his book? Isn't the partial-order relation of "is a subset of" (among others) important-enough to allow for partial orders?


* Rudin never formally-defined relation, just in case, tho let's assume a relation

on S is a subset of SxS with the above properties.

 

[micromass]

I suppose that it is sufficient for his goals. Certainly the subset relation is very interesting, but he probably doesn't need it anywhere in his book.

I guess he wants to stay close to the intuition of the order relation on the reals...

 

[Bacle2]

You may be right. Still, AFAIK, you need to work with set containment to prove, e.g., Hahn-Banach. Maybe he does that in his "Non-Baby" book.