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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.

Martin Sleziak
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Red Banana
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    Variables are used for all kinds of things. And I mean pretty much literally all kinds of things. – tomasz Jul 08 '12 at 02:54
  • 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. – Red Banana Jul 08 '12 at 02:55
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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 08 '12 at 02:57
  • 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" – Red Banana Jul 08 '12 at 02:59
  • 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 08 '12 at 03:03
  • I'm not very sure about the notation of these variables, supose I'm going to use a large number of variables, what should I do? $\star1,\star2,\star3...$? Of course I can invent a method, but I'm searching for common notation, so that people can understand what I mean. – Red Banana Jul 08 '12 at 03:17

2 Answers2

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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.

Qiaochu Yuan
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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.

Alex Becker
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