For $z =\frac{ xy}{x+y}$, why is $z < x$ and $z < y$ for all values of $x > 0$ and $y > 0$?
This question has to do with the concept of resistors, given two resistors in parallel the equivalent resistance is always lower than the smallest individual resistance, I am trying to convince myself that this is true.
The equivalent resistance is given by $z$ and the individual resistances are $x$ and $y$.