This is supposed to be the point where I throw up my hands and angrily tell you to study some math.

For what it's worth, I'm not sure what exactly your principle means because it hasn't been stated in math terms, but I can imagine only one math idea that could correspond to your vague statement, and that idea is self-evidently wrong. Namely, if you have a real-valued function defined on the positive integers and that function is strictly decreasing, you cannot reorder the values to make them strictly increasing. If you think that you can, I advise you to try building an example. For example, take f(n) = 1/n, which is strictly decreasing. Try to build a strictly increasing function g(m) such that for each m there's a unique n (and vice versa) satisfying g(m)=f(n). Both m and n range over the positive integers.

What's the reverse of the sequence 1,2,3,4...?