I'm currently reading a textbook for one of my classes (discrete mathematics), and we're doing set theory right now. This is not a question about how to do mathematics, it's about how to properly express through notation the concept I'm trying to convey. The text invites the reader to come up with a general formula for determining the cardinality of the union of an arbitrary number of sets, so here is what I have:(adsbygoogle = window.adsbygoogle || []).push({});

(Also, I did the best I could on the latex . . . I'm not that familiar with it)

[tex]

\left|\substack{n \\ \\ \Huge{\cup} \\ \\ k=1}\mathrm{S}_k\right|=\sum_{k=1}^{n}\left|\mathrm{S}_k\right|

-\left|\mathrm{S}_k \substack{n-1 \\ \\ \Huge{\cap} \\ \\ k=1} \mathrm{S}_{k+1}\right|+

\left|\substack{n \\ \\ \Huge{\cap} \\ \\ k=1}\mathrm{S}_k \right|[/tex]

I'm pretty sure it's standard practice, but if it's not, the bars mean "the cardinality of."

Okay so my question centers around the second term. I'm fairly certain that the way I wrote it is not how you'd write it. Is there a simple "iterate" operator that is like sigma but more general, so I could do something like ## \displaystyle \left(\substack{\scriptsize{n-1} \\ \Large{\mathrm{I}} \\ \\ \scriptsize{k=1}} \left| \mathrm{S}_{\small{k}} \cap \mathrm{S}_{\small{k+1}} \right|\right)## where ##\mathrm{I}## is the iterator? How would I write that?

Edit: And yeah, I'm aware that what I wrote down does not really work. Just had the question about notation.

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# A question about the proper use of certain notation

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