# Is there a formal definition for iteration?

I wanted know if there is a formal definition of iteration. In the sense that, this definition will say that after the 4th iteration is termination or the 5th iteration and not the 2nd iteration. Basically a rigorous definition of iteration.

• I would define iteration as tail recursion. – beroal Dec 15 '20 at 18:43

The $$k$$th iteration is just the $$k$$th element of some appropriate sequence. In general, I doubt it's a formally defined concept; it's just one of those things whose meaning is basically the natural-language meaning of the word.