This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Existence and uniqueness

When an entity or a concept in mathematics is introduced via a description instead of a direct computation, there is a possibility that this entity doesn’t even *exist*.

This means that there is nothing that satisfies the description. For example, “define $x$ as a number that satisfies equation $x+1=x$” produces nothing.

Similarly, when something is introduced via an iterative process instead of a direct computation, does it always make sense?

It’s possible that no matter how many iterations you run, you don’t get anything in particular (“divergence”). For example, “start with $1$, then add $1/2$, then add $1/3, 1/4$, etc” leads to unlimited growth with no end. (See harmonic series.)

In the case of iterations, the problem may be the lack of *uniqueness*.

Another term used here is "well defined", as in "well defined concept".