# What does the curly x symbol “$\mathcal{X}$” mean in “$\;x_i\in\mathcal{X}\;$”? [closed]

If you need more context, this equation is on the second page of this document. My guess is it just means "whatever value $$x$$ can have" or "all values of $$x$$", but I just wanted to check.

• It is just some set being used as a domain (if you refer to your article). – Anurag A Jun 28 at 21:31
• $x_i$ is an element of the set $\mathcal X$ ($\mathcal X$) – J. W. Tanner Jun 28 at 21:57
• The is answered just before the line you have highlighted (i.e. at the bottom of the left-hand column of page 2): $\mathcal{X}$ is just some domain from which the $x_i$ are drawn. The exact quote is "...where each instance $x_i$ belongs to a domain $\mathcal{X}$..." – Xander Henderson Jun 28 at 22:48
• You should delete the question, answer it yourself and accept the answer, or ask one of the commenters to post an answer, so the question does not attract attention as unanswered. – Ethan Bolker Jun 29 at 13:17
• I’m voting to close this question because it is too localized, and unlikely to be of general interest. – Xander Henderson Jun 29 at 17:51

Capital letters such as $$\mathcal{X}$$ (calligraphy "X") in the picture provided can be used to denote a set; in this case, it is. However, this is not always the case as $$f \subseteq \mathbb{R} \times \mathbb{R}$$ (lower case script "f") is sometimes used to denote a function on $$\mathbb{R}$$. You may also see capital letters used to denote an element of a set such as in the definition of the limit of a sequence for example. It just depends on context and the author of the literature.
• This is highly context dependent. In my line of work, calligraphic capital letters typically denote topological vector spaces. I think that your assertion that $\mathcal{X}$ usually denotes a set (without further structure) is quite strong, and is more absolute than is realistic. I am also not at all certain that I understand the relevance of anything you've written past the first sentence. – Xander Henderson Jun 30 at 4:53