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prove that 1>0

prove that 1>0

T13

How will i use axioms to prove that 1>0?

Reply 1

RichE

Original post by T13

How will i use axioms to prove that 1>0?

Depends somewhat on what axioms you've been given, but it is most likely to go something like:

(a) Precisely one of 1>0, 1=0 or -1>0 is true by trichotomy.

(b) 1=0 is untrue from the field axioms.

(c) -1>0 implies 1 = (-1)^2 > 0 by the order axioms and this contradicts (a).

(d) 1>0 is the only remaining possibility

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