I stumbled upon this question on Yahoo answers here :
Prove that for every positive real number x, l/x is also a positive real number.?
Answering to the question is [now] closed, but I was thinking about the answer, when I sketched this argument below, but am not sure if am right, and whether this could be a part of the required proof (or whether this is a mere echo of obvious statements?)
if $p$ is positive real number then this is true:
$p \ge 0 \implies |p| - p = 0$
A similar argument for negative number $n$ would be:
$n \lt 0 \implies |n| - n = 2|n|$
With the above truths, I can then say:
If $x \ge 0$ then ${1 \over x} \ge 0$ since $|{1 \over x} | - {1 \over x} = {0 \over x} = 0$
Is this right?