2

large curly x

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.

Blue
  • 75,673
slim
  • 149
  • 3
    It is just some set being used as a domain (if you refer to your article). – Anurag A Jun 28 '20 at 21:31
  • 1
    $x_i$ is an element of the set $\mathcal X$ ($\mathcal X$) – J. W. Tanner Jun 28 '20 at 21:57
  • 1
    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 '20 at 22:48
  • 1
    Ahh ok, I see that now. Should I delete this question? – slim Jun 29 '20 at 11:47
  • 4
    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 '20 at 13:17
  • 2
    I’m voting to close this question because it is too localized, and unlikely to be of general interest. – Xander Henderson Jun 29 '20 at 17:51

1 Answers1

1

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.

Taylor Rendon
  • 2,276
  • 2
    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 '20 at 04:53
  • @Xander Henderson - thank you for your feedback! I believe my emphasis on “usually used” in the context of notation was strong throughout my answer. Past my first sentence, I wanted to give a few examples of the usage of different lower case and upper case letters to denote different objects and defend my claim that it truly does, in fact, depend on what you’re reading in the first place. – Taylor Rendon Jun 30 '20 at 05:00
  • I edited my answer according to your suggestions, as well. – Taylor Rendon Jun 30 '20 at 05:13