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We use letters for unknowns/variables:

$x^2=4$

Are there variables/unknowns for operations too?

$8 \star 7 $

With the $\star $ being any operation.

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Variables are used for all kinds of things. And I mean pretty much literally all kinds of things. –  tomasz Jul 8 '12 at 2:54
    
I imagined it from the axiom: "If my naive mind could imagine that, then mathematicians mind's should've invented it at least 600 years ago". But I've never read something about it's usage. –  Vÿska Jul 8 '12 at 2:55
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600 years is a bit of an exaggeration. I don't think they used variables in quite the way we do nowadays, not even for numbers. But 100 years is probably a safe bet. –  tomasz Jul 8 '12 at 2:57
    
The nearest thing this request reminds me are the rings and groups, I guess it's a little related to what I'm searching: "A set, 1/2 operations - and these operations could be anything" –  Vÿska Jul 8 '12 at 2:59
    
That might be a bit of a long shot if you're not familiar with mathematics, but that general stuff probably belongs to model theory rather than algebra. –  tomasz Jul 8 '12 at 3:03

2 Answers 2

up vote 1 down vote accepted

Of course. For example, the Cayley-Hamilton theorem states that, if $a_nx^n+\cdots+a_1x+a_0$ is the characteristic polynomial of a linear operator $M$, then $M$ is a root of $a_nX^n+\cdots+a_1X+a_0$ where $X$ is a variable representing a linear operator (often called a matrix). A less common example (but probably more in the spirit of your question) is the Eckmann-Hilton argument, which shows that any two binary operators $\cdot$ and $\star$ which satisfy certain conditions are equivalent.

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But how to use it's notation? This is my doubt, this question is actually a step to another question. –  Vÿska Jul 8 '12 at 6:30
    
I'll the new question anyway - I'll just point the operators with text. –  Vÿska Jul 8 '12 at 6:31

Sure, but $\circ$ isn't a good choice; usually it denotes function composition. I would use $\star$, for example, which doesn't have an existing widely-used meaning.

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Oh, sorry. I don't know much about mathematics, and I imagined that the circle could mean something else, but I thought the context would let it clear for the readers. –  Vÿska Jul 8 '12 at 2:52
    
I switched it as you suggested. –  Vÿska Jul 8 '12 at 2:55

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