# Is there a formal way of representing N-elements-long comma-separated lists of elements?

I frequently find myself in a situation where I want to express a comma separated list of $N$ elements, for example $Z_i$ where $i \in \{1,2,...,N\}$, which people often write as $Z_1, Z_2, ..., Z_N$.

However, I am not a fan of that notation because it takes more characters than would seem necessary; i.e., all that matters is that there is a set of $N$ $Z_i$ values. Is there a formal notation which I am missing?

• I have seen many people using programming notation. I personally use $i \in [1..N]$ which I have inherited from Pascal. I have seen people do the same for matlab, i.e. $i \in [1:N]$. But yeah, it would be great to know if anybody has formalized it. – Aleksejs Fomins Feb 21 '18 at 19:51
• One way is to describe it in words as an $n$-tuple. This still requires the reader to follow the context and remember the number of $Z_i$, but at least it is a way to keep the writing short. For example: "Consider an $n$-tuple $Z$ of complex numbers. Then..." – Théophile Feb 21 '18 at 19:54
• Even if you find out here that "someone" has formalized it you will still have to define the formal notation in your document, since it won't be a common one. So pick a short one you like, define it locally, ans use it. – Ethan Bolker Feb 21 '18 at 19:55
• There are many ways of doing it, and no consensus standard. Bottom line: Use one of the many accepted alternatives, and be consistent. If you choose a less readable version, explain its meaning when first used. – quasi Feb 21 '18 at 19:55