What is the mathematical term for an operation that is self reversing?
For example:
- Multiplying by -1
- 1/x
In general:
f(f(x)) = x
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6It's an involution. – mathreadler Feb 21 '16 at 11:03
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Great. That will do. Although, I was hoping it was a word I had heard of! – rghome Feb 21 '16 at 11:09
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We call them involutions.
They can range from something as straightforward as a reflection to complicated functions like $$f(x)=\ln \left (\frac{e^x+1}{e^x-1} \right )$$ where $x>0$.
I'd also like to note that the notion of the involution extends beyond just functions and are quite useful in topics of abstract algebra such as group and ring theory.
The above example is also in the Wikipedia link below.
Link below for more: https://en.wikipedia.org/wiki/Involution_(mathematics)
Trogdor
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When speaking of two's complement and XOR, would we also call these involutions? – mckenzm Mar 08 '20 at 05:45