SOLUTION: Looking for a Proof to the theorem that given x>c, then 1/x < 1/c for any Real numbers x and c. Thanks, Gary

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Question 260233: Looking for a Proof to the theorem that given x>c, then 1/x < 1/c for any Real numbers x and c.
Thanks,
Gary
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
let's start out with the opposite
1/x>1/c
multiply both sides by x
1>x/c
multiply both sides by c
c>x
but that can't be since we are given that x>c
so the assumption that 1/x>1/c must be wrong there fore 1/x<=1/c
so now we have to show that 1/x can't be equal to 1/c
1/x=1/c
1=x/c
c=x
but that can't be either since we are given that x>c
so 1/x<1/c