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When you read a formula aloud you say "r and r-star are related by this formula". If you write this formula down you normally write an r with a six-handed star, which would actually be an asterisk and not star (with 5 sharp hands) because it's easier to draw by hand.

But what to do when typing this formula in LaTeX? Should I set it as I pronounce it?

r^\star = a r

Or as I write it by hand?

r^\ast = a r

And will \ast always do the same as *?

r^\ast == r^* %???

Is one (\star or \ast) simply wrong (typographically or semantically) or is it just a matter of personal preference?

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My answer would be "neither": it is a matter of conventions, depending on the specific mathematical meaning and on the uses of the field. There are contexts in which people use stars, and contexts in which they use asterisks. Check the books and papers that are relevant to your application, and I am fairly sure that they will always use the same symbol. – Federico Poloni Nov 10 '12 at 12:50
One is pronounced "convolution" and the other "cross-correlation". ;) Note that the asterisk can print as a 5-pointed star in sans-serif fonts even if it prints as a 6-pointed star in serif fonts. – endolith Apr 9 '14 at 16:42
up vote 17 down vote accepted

I think it's just personal preference. In the standard setup * and \ast are the same.

fontmath.ltx has

\DeclareMathSymbol{*}{\mathbin}{symbols}{"03} % \ast

So both pick up character 3 from the symbol font with infix binary operator spacing.

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but \star also exists (in some fonts) and it does mean something entirely different from * or \ast (although it's "usual" to say "star* when verbalizing the math operator or the most frequently used super/subscript symbol). – barbara beeton Nov 10 '12 at 13:31

At the character level, there are several star-like symbols, but the most common are:

U+002A ASTERISK “*” is the well-known Ascii character with multiple and vague semantics. In mathematics, it is often used as a unary postfix operator or modifier (e.g., N* denotes the set of natural numbers without zero), and its appearance in most fonts is superscript-like, at least somewhat above the baseline of text. In LaTeX math mode, you cannot write it directly, as it gets displayed as asterisk operator. Use mbox{*} instead or, if you prefer a larger size for the symbol, ^{*}. I would expect that this is what you need for “r-star”.

U+2217 ASTERISK OPERATOR “∗”, classified as a mathematical symbol. It is generally placed vertically near the middle of the x-height, like “+”, “×” etc. are. It is the standardized symbol for convolution operator, and it has many specialized uses. It can be identified with the symbol that the normal Ascii asterisk “*” character produces in LaTeX math mode. It can be written as \ast if desired.

U+22C6 STAR OPERATOR “⋆”. This has no generally standardized usage, but it is classified as a mathematical symbol. It, too, is generally placed vertically near the middle of the x-height. It can be identified with \star in LaTeX.

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