> Hence, a question like this may not have a unique right answer. If you allow philosophers in, you will definitely not have a unique answer :)
I'm not sure if this is what you're describing, but many nonlinear[1] math problems have no closed form solution[2]. That means you can't use any regular function, all the operators and the infinitely real numbers to describe every solution: you can only use the infinitely real numbers to describe one solution.
I've written a blog post on this topic[3]; that blog post works through all the underlying stuff before getting to these closed form solutions.
I'm not sure if this is what you're describing, but many nonlinear[1] math problems have no closed form solution[2]. That means you can't use any regular function, all the operators and the infinitely real numbers to describe every solution: you can only use the infinitely real numbers to describe one solution.
I've written a blog post on this topic[3]; that blog post works through all the underlying stuff before getting to these closed form solutions.
[1]:https://en.wikipedia.org/wiki/Nonlinear
[2]:https://en.wikipedia.org/wiki/List_of_nonlinear_partial_diff..., https://en.wikipedia.org/wiki/Closed_form_solution
[3]:http://scottsievert.github.io/blog/2014/07/31/common-mathema...