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I was looking at the list of "unary operators" on https://en.wikipedia.org/wiki/Unary_operation, and I found that it does not include exponents, e.g., $4^2$. Are exponents not considered unary operators because technically something like $4^2 = 4 * 4$, which is a binary operation?

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$x^2$ is and $4^x$ are both unary operations. And the article you cited states "An example is the function f : A → A"

So all single value real functions are unary operators. If the article didn't mention exponents or power functions specifically it's only because it didn't consider them worth mentioning.

fleablood
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