Given a binary operation $\ast$ on integers at least $2$, define $\ast'$ by $$m\ast' n = \overbrace{m\ast m\ast \cdots \ast m}^{n\text{ times}}.$$

Example :

• if $*$ is $+$ , $*'$ is $×$. Multiplications are a lot of additions.

• if $*$ is $×$ , $*'$ is $^$. Exponential are a lot of additions.

The question is what's $*'$ when $*$ is $+$ ?

Additions are a lot of... what ?

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Successor operations. But the successor operation is a unary operation. –  Daniel Fischer Sep 14 '13 at 19:29
So in a sense "successor operatioans" is right, but it doesn't answer the question since it's a unary operation. –  Michael Hardy Sep 14 '13 at 20:09