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Topic: mediant of two integers
Replies: 12   Last Post: Aug 23, 2013 2:57 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: mediant of two integers
Posted: Aug 17, 2013 9:44 PM

Joshua Lindman <i.love.jeevitha@gmail.com> wrote:

> What is the most general form of the median inequality?

Do you mean median or mediant?
>
> Let a/b < c/d (rationals, where a,b,c,d integers)
>
> Then,
>
> a/b < (a+c)/(b+d) < c/d
>
>
> I don't see any restrictions on a,b,c,d (except that b,d nonzero) in
> Wikipedia:
> http://en.wikipedia.org/wiki/Mediant_%28mathematics%29

Note that there is a difference between medians and mediants.

The standard definition of MEDIAN for an even number of numerical values
is halfway between the middle two in order of size.
So for two values, their median and their mean coincide.

The median of a/b and c/d, with non-zero denominators would be
their average value, (a/b + c/d)/2
--

Date Subject Author
8/17/13 i.love.jeevitha@gmail.com
8/17/13 Virgil
8/17/13 William Elliot
8/17/13 i.love.jeevitha@gmail.com
8/18/13 William Elliot
8/18/13 i.love.jeevitha@gmail.com
8/18/13 William Elliot
8/23/13 i.love.jeevitha@gmail.com
8/18/13 quasi
8/18/13 i.love.jeevitha@gmail.com
8/18/13 quasi
8/18/13 Virgil
8/23/13 Karl-Olav Nyberg