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I have seen authors use $\star$, $\ast$, $\cdot$ and $\odot$ to represent arbitrary binary operations on sets. I'm wondering, what is the standard way to read or pronounce something like $a \star b$? How would you read $a \odot b$?

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How about "a odot b"? :P –  Bruno Stonek Mar 30 '11 at 1:08
    
I guess what I'm trying to ask is, is there a standard way to say $a \Box b$, where $\Box$ is meant to represent some arbitrary operation? Saying "a operation b" doesn't really flow. –  Zach Langley Mar 30 '11 at 1:14
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For an unspecified (or strange) operator, I would say "times" or "composed with". –  Jack Schmidt Mar 30 '11 at 1:17
    
@Jack: "composed with" seems inappropriate if the operator isn't associative. –  Qiaochu Yuan Jul 29 '12 at 7:32
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3 Answers

up vote 4 down vote accepted

Usually, when I write such an operator into a problem, I use some variant of an asterisk or star (often a circled asterisk), reading it as "star" in my head. If I'm not using some sort of star, I usually use a circled or boxed X-type symbol and read it as "cross" in my head.

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I try to read from the context what it's supposed to mean. Most of the time I can extract how it's pronounced by just looking at the preceding text.

Without context I read $\odot$ as tropical multiplication and $\star$ as convolution (of some kind), but of course they can represent some other binary operation just as well. For $\cdot$ I could use either dot or times and $*$ could be times or star, I guess.

But most of the time there is a context, isn't it? If not, then my main priority would be to try and find the context.

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What if the context is only that is it an operation? For example, "Given a binary operation $\diamond$ that is associative and commutative, show that..." –  Zach Langley Mar 30 '11 at 14:29
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Then I would pronounce it as it looks, i.e. star, dot, square and perhaps "circled dot" for $\odot$ –  Elin G Mar 30 '11 at 16:32
    
Yeah, I would say the operation itself. "ƒ∗g" uses the "asterisk operator", for instance, but in the context of engineering, I would not say "f asterisk g" or "f star g". I would say "f convoluted with g" or "the convolution of f and g". In other contexts, the same symbol would be read differently. –  endolith May 17 '11 at 15:42
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I suggest "sun" for $\odot$ (the standard astronomical symbol).

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