I came across the following notation in a research paper

Suppose we have a function $f(x) \in [1,l] \rightarrow \mathbb{R}$

It is the first time, I am looking such a notation. And the paper is using the same notation for all functions used in it.

Is it same as $f(x) : [1,l] \rightarrow \mathbb{R}$

If yes, is it an abuse of notation?

If no, what does the notation mean?

  • 5
    $\begingroup$ What a weird notation. $\endgroup$
    – azif00
    Feb 15, 2021 at 9:08
  • 1
    $\begingroup$ It would probably be helpful if you gave some idea of when the paper was published (decade identification is probably enough -- 1950s, 1960s, 1970s, 1980s, etc.) and gave the name of the journal. For instance, I would imagine this would be more peculiar if published in Transactions of the AMS in the 1990s than in some mostly unknown journal less than 20 years old. $\endgroup$ Feb 15, 2021 at 11:10
  • $\begingroup$ @DaveL.Renfro It is a recent paper, around 2016... $\endgroup$
    – hanugm
    Feb 15, 2021 at 11:25
  • $\begingroup$ It must be stressed that $f(x)$ is not a function. $f$ is. $\endgroup$
    – K.defaoite
    Feb 23, 2021 at 3:25

1 Answer 1


In the paper you're using, I understand it means that $f$ belongs to the set of all functions defined from the set $[1,l]$ to the set $\mathbb{R}$, to be said, $$[1,l]\to\mathbb{R} := \{f \text{ function }: f \text{ is defined from $[1,l]$ to $\mathbb{R}$}\}$$ so it works the same way as defining $f$ the usual way, to be said: $$f\in[1,l]\to\mathbb{R} \equiv f:[1,l]\to\mathbb{R}$$

  • 3
    $\begingroup$ @iftiben10 that is not the way you should upvote. Upvotes must be given when you consider a post deserves it, not just for mindlessly earn reputation asking users you upvoted to upvote you in return. $\endgroup$ Feb 15, 2021 at 9:04
  • $\begingroup$ sorry, brother, I'm a sad person that my question doesn't have many votes thank you for your response. $\endgroup$
    – iftiben10
    Feb 15, 2021 at 9:07

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