prove that a<(a+b)/2 for any two rational numbers a and b,where a<b.
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If a is rational, and b is rational, then (a+b)/2 is rational. To prove it, assume a=p/q, b=r/s, and p, q, r, s are integers; then (a+b)/2=(ps+qr)/(2qs), which is the quotient of two integer expressions, and thus also a rational
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