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

Existence and uniqueness

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.
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.)