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I'm studying a number of highly cited papers and I read the following notation:

$$\mathbb{1}_{d\in D}$$

which, from my understanding, is a shortcut for $\mathbb{1}_D(d)$ where $\mathbb{1}$ is the indicator function. In another paper, I found another notation for an indicator random variable:

$$\mathbb{1}\{X_1,\ldots,X_n\}$$

where $X_1,\dots,X_n$ are elements of a set.

I could not find any evidence about such ways to write indicator functions. In the first case, I don't think that writing $\mathbb{1}_{d\in D}$ is more readable than $\mathbb{1}_D(d)$. In the second case, a possible explanatio is that $$\mathbb{1}\{X_1,\ldots,X_n\}$$

is more readable than

$$\mathbb{1}_{\{X_1,\ldots,X_n\}}$$

Since these are prominent papers written by well-known scientists, I'm afraid that I'm missing something. Do you know why people use these alternative notations?

Thanks!

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  • $\begingroup$ The choice of a good notation can also depend on the context, but sometimes its just different personal preferences, or whatever is popular in that particular field. Since we do not know the context, this question is hard to answer precisely $\endgroup$
    – supinf
    Nov 27, 2020 at 15:12

1 Answer 1

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The reason that people use alternative notations is because there is no/little consensus in some areas of mathematics. Note, that mathematics is the science that deals with logic and arrangements. Moreover, it is all around us. Whether or not you believe that mankind had a single origin, by the time humans started writing, in particular writing down mathematics, they were well spread out over our globe. These groups of humans all had there own language and symbols. The aftermath, pun intended, can still be seen today. One can only hope the consensus in mathematical symbols increases over time. However, in particular fields, like machine learning, they often do not really care about the notational integrity.

I think you hoped for a different, more rational, reason but I do not believe there is any.

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