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b0it0i

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**Analysis problem: x>o --> 1/x > 0**

## Homework Statement

Prove

If x>0 --> 1/x > 0

## Homework Equations

ordered field axioms

closure, associativity, commutativity, identity, inverses, distributive law, trichotomy law, transitive law, preservation

x+z = y+z --> x = y

x.0 = 0

-1.x = -x

xy=0 iff x=0 or y=0

x<y iff -y<-x

x<y and z<0 then xz > yz

## The Attempt at a Solution

i've tried this problem several times, and always hit a dead end

i tried a direct proof

assume x>0

therefore x does not equal 0

by existence of inverse

there exists a unique 1/x such that x (1/x) = 1

after that point, i get no where in my attempts

any suggestions?

you can user other "theorems" but you must also prove them