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When we define a structure, let's say a group, we write $(G ,\oplus )$ for an operation $\oplus$. In case I want to define a structure with operation exponentiation I just define the $\oplus$ so that $a \oplus b = a^b$, which is what I have done until now. But a curiosity of mine is, if there exists, or if it ever existed, a symbolic representation of exponentiation.

Thus, have you ever come across a symbol for exponentiation?

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    $\begingroup$ What about the up arrow $\uparrow$ ? $\endgroup$ – Yves Daoust Feb 11 '15 at 14:16
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Generally the caret ( ^ ) symbol and (as Yves mentioned) the up arrow ( ↑ ) is used for exponentation.

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  • $\begingroup$ I suppose, after reading the Wikipedia article on the arrow notation, that this latter is usually preferred to the first one, or is it just a matter of personal preference? $\endgroup$ – eslukas Feb 11 '15 at 14:19
  • $\begingroup$ Where did you read it? @E.S.L. $\endgroup$ – Kunal Gupta Feb 11 '15 at 14:24
  • $\begingroup$ If I understood correctly, the use of the caret in order to express exponentiation comes from programming languages implementation, whereas the up-arrow is a more formal version of it. I might be wrong, I am just conjecturing. $\endgroup$ – eslukas Feb 11 '15 at 14:37
  • $\begingroup$ I have seen both in programming. $\endgroup$ – Kunal Gupta Feb 11 '15 at 14:43
  • $\begingroup$ Here: en.wikipedia.org/wiki/… <-Usage of caret $\endgroup$ – Kunal Gupta Feb 11 '15 at 14:48

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