# How to deduce the last inequality ;( [duplicate]

Julián Aguirre gave a simple-amazing answer for this question: How to prove this property using convexity?

Unfortunately, i don't understand how to deduce the last inequality $$a+b-c<(a+b)/2$$.

Somebody help me. I don't know what I'm missing.

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He is trying to show that if the result is true for all convex functions (with no assumption on monotonicity if $$f''$$ then there is another convex function $$g$$ for which the new $$c$$ (which is $$a+b-c$$) is less than $$\frac {a+b} 2$$. Hnec the result cannot be true with just convexity.