2 ordered field theorems that need proving
My textbook has kindly decided to present twotheorems without proof, meanwhile all others have proofs. I don't want to come up with a flawed proof, so I need some help.
The first of the two involved proving that 0 =/= 1
I did this one, with the help of mhf.
The remaining theorem will probably incorporate the latter into its proof...
Def. a < b <=> a<=b and a =/=b
Thm. For any ordered field, 0 < 1.
I'm not really sure where to start, contradiction seems like it's the way to go...
Suppose that for some ordered field, 1 <= 0
0 =/= 1, so 1 < 0
by another theorem that i've proved already, (-0) < (-1)
but (-0) = 0 < (-1)
and... i feel like i'm going in circles, please help