Re: Inequality with max I want to understand

neillclift@xxxxxxx wrote:

Hi,

I was reading a paper and hit an inequality I have never seen before:

(a + b) / (c + d) <= max (a/c, b/d)

It's the _mediant_ of fractions:

http://en.wikipedia.org/wiki/Mediant_%28mathematics%29

In the paper I have the additional constraints that c > 0, d > 0, a >=
0, b >= 0.
I am interested in where this comes from and other examples. If there
are
books or other resources that contain stuff similar to this I would
like to know.
I have no idea how I might search for something like this online for
example.
I haven't sat down yet for an extended period to try and prove this.
I don't really have an idea of how to try and tackle it either.
Mathematica can find counter examples with negative variables but not
with the additional constraints.

An interesting application of mediants is the Stern-Brocot tree:

http://en.wikipedia.org/wiki/Stern-Brocot_tree

Han de Bruijn

.

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