# Notation For Collection of Mutually Exclusive Subsets

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\$$

• Have you seen this: math.stackexchange.com/questions/2170945/… – Colm Bhandal Oct 9 '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 9 '20 at 12:38
• It looks meaningless to me. – Andrés E. Caicedo Oct 9 '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 9 '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 9 '20 at 15:42

• 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 9 '20 at 15:34
• @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 9 '20 at 16:31