How to reorder a vector with calculus from max to min for an order-specific summation using calculus?

Question

I have a vector $V$ containing a set of finite numbers ranging between $0.0$ and $1.0.$

However, they may not be in consecutive order. How can I reorder them with a calculus formula? Even better, is how to make them in reverse order (max to min)?

I need the vector (set of numbers) to be in the correct order to apply a function to them where order is important.

Answer 1

There is no simple formula for this. In a theoretical argument you can just say "Let $a_{\geq}(x)$ be the $n$-tuple obtained from $x=(x_1,x_2,\ldots, x_n)$ by arranging the $x_k$ in descending order". If, however, you have to pass over the entries $x_k$ in a computer program in descending order you have to set up or recurse to an algorithm accepting the $n$ tuple $x$ as input and outputting the $x_k$ in descending order. If $n$ is large this is a science of its own kind.