This isn't homework or anything. I'm just interested in learning to prove things in mathematics, so I took a piece of paper and did the following:(adsbygoogle = window.adsbygoogle || []).push({});

For every a < b it is true that a < (a+b)/2 < b (1). First I separated the inequality: a < (a+b)/2 and (a+b)/2 < b. Then I did this:

a < (a+b)/2

2a < a + b

2a - a < b

a < b

and

(a+b)/2 < b

a + b < 2b

a < 2b - b

a < b

So for the inequality (1) to be true, it must be true that a < b. So we have proven the statement in the first sentence.

Right? Wrong? Not rigorous enough?

- Kamataat

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# Proof help

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