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bonfire09
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Homework Statement
Prove that for every two distinct real numbers a and b, either (a+b)/2>a or (a+b)/2>b
Homework Equations
The Attempt at a Solution
Proof:
if two distinct numbers a and b then (a+b)/2>a
Since a≠b and a,bεR, (a+b)/2>a=a+b>2a=b>a. Therefore (a+b)/2>a if b>a.
and
if two distinct numbers a and b then (a+b)/2>b
Since a≠b and a,bεR, (a+b)/2>b=a+b>2b=a>b.
Therefore (a+b)/2>b if a>b.
would this suffice as a proof or no?
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