- #1
Buri
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Hi I've looked up the definition of an ordered field and I've found two slightly different ones. One is that an ordered field is a field with a total order, but I've found another which requires it to also satisfy:
(1) If a <= b then a + c <= b + c
(2) If 0 <= a and 0 <= b, then 0 <= ab.
Which one is the correct one? And could someone give me an example of a field which has a total ordering but doesn't satisfy the extra conditions? Thanks I'd appreciate it :)
(1) If a <= b then a + c <= b + c
(2) If 0 <= a and 0 <= b, then 0 <= ab.
Which one is the correct one? And could someone give me an example of a field which has a total ordering but doesn't satisfy the extra conditions? Thanks I'd appreciate it :)