Virgil
Posts:
8,833
Registered:
1/6/11


Re: mediant of two integers
Posted:
Aug 17, 2013 9:44 PM


In article <5a4bcddb6e7443249491bf71bfaf5b83@googlegroups.com>, 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 nonzero denominators would be their average value, (a/b + c/d)/2 

