2

I have a set $K$ that is formed by mutually exclusive subsets $k_1..k_n$. Can I express it using following notation?

$$ \biggr\rvert^{h=n}_{h=1} k_h \subset K\ $$

Eric Wofsey
  • 330,363
GENIVI-LEARNER
  • 534
  • Have you seen this: https://math.stackexchange.com/questions/2170945/what-is-the-mathematical-notation-for-a-group-of-pairwise-disjoint-sets – Colm Bhandal Oct 09 '20 at 12:13
  • @ColmBhandal Thanks,I see it now, but I also want to know if the notation I wrote is correct or not. – GENIVI-LEARNER Oct 09 '20 at 12:38
  • 2
    It looks meaningless to me. – Andrés E. Caicedo Oct 09 '20 at 13:38
  • @AndrésE.Caicedo, could you please elaborate? What it is being implied in the notation that each $k_h$, with $h$ ranging from ($1..n$) is the subset of $K$, I couldnt find more simple notation to illustrate this. Could you please let me know why is this meaningless. – GENIVI-LEARNER Oct 09 '20 at 13:51
  • I couldnt find more simple notation to illustrate this. --- Why not just write the following? "Let $k_1,$ $k_2,; \ldots, ; k_n$ be pairwise disjoint subsets of $K.$" Incidentally, if you intend for each of these subsets to be nonempty, then you need to additionally specify this, such as by writing "$\ldots$ pairwise disjoint nonempty subsets $\ldots$". – Dave L. Renfro Oct 09 '20 at 15:42

1 Answers1

1

Well, you can use whatever notation you want, as long as you clearly define it. But this is not a standard notation, and so no one will understand it unless you define it for them. In particular, I have never seen a vertical bar used to indicate any meaning remotely similar to this one.

Eric Wofsey
  • 330,363
  • A sub- and super-scripted vertical bar is often used when evaluating a definite integral over a compact interval by the Fundamental Theorem of Calculus, but that's not what I would call similar to this usage (thus, I agree with you), so I agree that the present notation is not sufficiently well known (if "known" at all) to use without explicitly defining it. Also, part of this notation is similar to that used in summations and products, and vertical bars are often used in writing sets (e.g. ${x \in {\mathbb R} , | ; x^3 + x < 5}),$ but I've never seen these two combined in this way. – Dave L. Renfro Oct 09 '20 at 15:34
  • May I know what would be more suitable notation to convey what I am trying to convey using vertical bar and limits? – GENIVI-LEARNER Oct 09 '20 at 16:18
  • @DaveL.Renfro, I simply took it from calculus indeed where the vertical bar showed the limits for intergral so I guess I shouldnt use such notation here as it is unheard of. – GENIVI-LEARNER Oct 09 '20 at 16:20
  • 1
    @GENIVI-LEARNER: I don't know any suitable notation that uses a vertical bar. One fairly standard notation would be $K=\bigsqcup_{h=1}^n k_h$. – Eric Wofsey Oct 09 '20 at 16:31
  • @EricWofsey, noted but the union notation will not convey that all the $k_h$ are mutually exclusive – GENIVI-LEARNER Oct 09 '20 at 16:35
  • 1
    @GENIVI-LEARNER: Wofsey is using this symbol. However, I don't think it's sufficiently well known to use without defining it. Anyway, is there a reason for needing such a symbol? If you only plan to use it a few times, you'll just be creating additional symbol-clutter, which makes reading a chore because your reader will have to digest and interpret all the symbols. FYI, there are often questions at this site that I'll click on, see a wall of symbols, and immediately use the "back button" because I don't feel like trying to decipher the code. – Dave L. Renfro Oct 09 '20 at 16:52
  • @DaveL.Renfro +1 Thanks a lot for clarification! I really thought it would be quite brief and simple to mention what I had mentioned. But I understood that additional symbol-clutter would be undesirable. – GENIVI-LEARNER Oct 09 '20 at 17:35
  • @GENIVI-LEARNER: FYI, the issue of "symbolic rendering" came up in a mathoverflow question the other day. In my comment there I wondered whether it was really necessary to have the notation requested, and I gave an example of how the notation asked for might actually be useful. However, I don't know whether the OP actually needed the notation for some purpose like the example I gave, or whether the OP simply thought the additional notation would provide more mathematical rigor, which in the latter case I didn't think so. – Dave L. Renfro Oct 09 '20 at 17:47