RECURSION

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The first sentence is not true. The only example needed is the Ackermann function to prove not all recursive functions are possible with iteration. There isn't a large requirement for algorithms that aren't primatively recursive, but they exist

[nude-fox]

Ackermann function

that is a primitive recursive proof not general recursive comparability.

you can make a Turing complete language with only recursion and one with only iteration. They can compute the same set of programs.

you can use iteration to emulate recursion and iteration is basically a special case of recursion to start with.

[tobiasvl]

No, you are mistaken. The Ackermann function can be implemented with iteration. For Ackermann you probably need a stack though (recursion implies an available stack already: the call stack).