$g:[0,1]\to[0,1]$ continuously differentiable and increasing such that for
   all integers $t&gt;0$ and for all $r\in(0,1)$, $g(r^{t+1})&gt;g(r)\cdot g(r^t)$. Does this imply
   that for all $r\in(0,1)$, and $m,n \in N$, $g(r^{m+n})&gt;g(r^m)\cdot g(r^n)$?
  If not, what can be a counter example?


This is the last part of a larger question that I had asked before here: http://math.stackexchange.com/questions/810277/a-unsolved-puzzle-from-number-theory-functional-inequalities. Overcoming this would help me solve the whole question.

Edit: I missed this out, when I posted initially: $g(0)=0$ and $g(1)=1$


Question: How do I find which elements in one array aren't in another?
Answer: See the FAQ How do I compute the difference of two arrays? How do I compute the intersection of two arrays?

Adapting the code you posted:

#!/usr/bin/perl

use strict; use warnings;

my @x = 1 .. 10;
my @y = grep { $_ % 2 } @x;

my %lookup = map { $_ =&gt; undef } @y;

for my $x ( @x ) {
    next if exists $lookup{$x};
    print "$x\n";
}