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Original question: The symbol looks like a numeral 1 written like an R in $\mathbb{R}$. It has a double vertical line and a serif at the bottom. It represents a function of a parameter: $1_{\{0,1\}}(x)$. Adding it as a factor to your formula limits your expression to a specific set or range of x values. In my example, if x is neither 0 nor 1, the whole expression is zero. Like a security switch against over- or underflow of your parameters.

What is it called, please? (I want to learn more about it, but I cannot talk about it without a word for it).

Answer: Thank you! Now I have two names for it:

  • Characteristic Function and
  • Indicator Function

In English, an indicator function is a characteristic function, so I will use the word indicator function from now on, as it is the specific usage I was looking for.

To type it in TeX, thanks, I have learned to add package bbold and then mathbb{} the number 1. So that marginal hitch is history, too.

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  • $\begingroup$ Use the detexify webpage and you find code for it. $\endgroup$
    – KConrad
    Commented Aug 16, 2015 at 0:25
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    $\begingroup$ tex.stackexchange.com is where this question belongs. $\endgroup$
    – Nate Eldredge
    Commented Aug 16, 2015 at 0:26
  • $\begingroup$ See tex.stackexchange.com/questions/488/blackboard-bold-characters $\endgroup$
    – Nate Eldredge
    Commented Aug 16, 2015 at 0:28
  • $\begingroup$ Sorry, the question still has only the wrong tag. I am not asking about TeX, I want to ask about the symbol, talk about that symbol and its usage, but how can I do that, when I only know how to write it manually? Also, \mathbb{1} is not what I need. $\endgroup$
    – AOphagen
    Commented Aug 16, 2015 at 0:29
  • $\begingroup$ Nate: thanks, adding package bbold at least enabled me to type that one symbol. Now I still need a name to call it, so I can properly talk about it, and a proper tag for this question. $\endgroup$
    – AOphagen
    Commented Aug 16, 2015 at 0:36

1 Answer 1

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The function $\mathbb 1_A$, whose values are $1$ for arguments in the set $A$ and $0$ for arguments outside $A$, is usually called the characteristic function of the set $A$.

Unfortunately, the same terminology is also used with other meanings. For example, in probability theory, "characteristic function" often means the Fourier transform of a probability distribution.

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    $\begingroup$ Another commonly used term for this concept is "indicator function". $\endgroup$
    – Tobias Fritz
    Commented Aug 16, 2015 at 0:44
  • $\begingroup$ Yes, I think when I first saw that symbol, the prof mentioned "indicator function" just once. I forgot. :( Is "indicator function" also used in other circumstances, like "characteristic function". If I learn a word for it now, a nonambiguous one would be much better. $\endgroup$
    – AOphagen
    Commented Aug 16, 2015 at 0:49
  • $\begingroup$ In convex analysis the term indicator functions is used for a function that is zero in some set and plus infinity elsewhere. $\endgroup$
    – Dirk
    Commented Aug 16, 2015 at 9:36

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