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Let $\{a_1,a_2,\dots,a_n\}$ be an ordered set.

Is there any established mathematical notation for the first $k$ (resp. last $k$ ) elements of this ordered set?

This corresponds to the computer science equivalent of "substring".

Thanks.

yoyostein
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    There isn't even an established mathematical notation for "ordered set". "List" is common, but that's more cs than math. "Ordered $n$-tuple" is standard, but it limits you to exactly $n$ objects. – vadim123 Feb 08 '18 at 05:59
  • There's an established notation that ${a_1,a_2,\ldots,a_n}$ denotes a set, not an ordered set. – Angina Seng Feb 08 '18 at 06:54
  • It looks like you're talking about finite sets, so in your case an ordered set $X$ is essentially a set $X$ with an order function (bijective) $f:X→{x\in N^+ | x<|X|}$, i.e. just a sequence. – Al.G. Apr 08 '19 at 21:14
  • @AI.G. with that definition there would be nothing stopping any element from X be put in the same position $x \in N^+$, would there? – stimulate Sep 11 '22 at 13:41

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You could say the following. Let $a_1 < a_2 < \ldots < a_n$ be a chain. For $1 \leqslant k \leqslant n$, the chain $a_1 < a_2 < \ldots < a_k$ is called the prefix of length $k$ of the original chain. Its suffix of length $k$ is the chain $a_{n-k + 1} < \ldots < a_n$.

J.-E. Pin
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