Take the 2-minute tour ×  Suppose we have 4 functions depending
on a variable x : $a(x), b(x), c(x)$ and $d(x)$.  I want to
prove that $a(x) - c(x)$ is monotonically increasing in $x$, by
an induction argument. Also I want to as well prove the same
result for $b(x) - d(x)$.  In my derivations I obtain the
following equation:  $a(x+1) - c(x+1)$ = $constant_1$
*$(\min(a(x), b(x)) - min(c(x), d(x)))$   $b(x+1) - d(x+1)$ =
$constant_2$ *$(\min(a(x), b(x)) - min(c(x), d(x)))$  My
question is if I claim that $a(x) - c(x)$ is increasing in x,
also $b(x) - c(x)$ is increasing in x - then $(\min(a(x), b(x))
- min(c(x), d(x)))$ is increasing in x?  I am not sure about
this type of induction argument as it requires 2 conditions to
happen at once for it to be true. Could that be an example of
double induction though?   share|improve this question please
use LateX formatting. –  nbubis Mar 5 '13 at 22:50 The proof
does not work unless you can show more abot $a,b,c,d$. For
example, even if $c_1=1000$, then you might have $