Template:MSeq

Purpose

I very often have to write $(A_n)_{n=1}^\infty$, and sometimes get lazy and just write $(A_n)$ instead. To solve this I shall introduce this template:

• Template:MSeq - for "Mathematical sequence"

Caveats

1. For $({ A_n })_{ n = 1 }^{ \infty }$ you must provide A_n for the first parameter, even though it knows the index is n, this is because of subsequences, if we have A_n as the sequence representation, and use j as the index, as in $({ A_{n_j} })_{ j = 1 }^{ \infty }$ this would be rendered as:
   • {A_n}_{j}, yielding ${A_n}_j$ not $A_{n_j}$ (A_{n_j}) as intended.

Parameters

The parameters are ordered (except for the in one)

Parameter	Name	Default	Meaning
1	(no named equiv)	A warning about the lack of value	The representative element of the sequence shown in brackets, in $({ A_n })_{ n = 1 }^{ \infty }$ is is A_n
2	index	n	The indexing variable, used for the "$n$" in the "$n=1$" part of $({ A_n })_{ n = 1 }^{ \infty }$
3	from	1	The starting index of the sequence, eg the "1" in the "$n=1$" part of $({ A_n })_{ n = 1 }^{ \infty }$
4	to	\infty	The end index, eg the "$\infty$" in $({ A_n })_{ n = 1 }^{ \infty }$
(no index)	in	to say a "sequence in $X$" means the sequence consists of elements of $X$, see abuses of the implies-subset relation for more. Represents the "$\mathcal{X}$" in $({ A_n })_{ n = 1 }^{ \infty }\subseteq \mathcal{X}$
(no index)	pre	Any math-markup preceding the sequence, eg the $\exists$ in $\exists ({ A_n })_{ n = 1 }^{ \infty }$
(no index)	post	Any math-markup after the sequence, eg the $[A_i<C]$ in $\forall i\in\mathbb{N}\exists ({ A_n })_{ n = 1 }^{ \infty }\subseteq X [A_i<C]$

Examples

• {{MSeq|A_k|k}} - $({ A_k })_{ k = 1 }^{ \infty }$
• {{MSeq|A_k|index=k}} - $({ A_k })_{ k = 1 }^{ \infty }$
• {{MSeq|A_p|p|5|105|in=\mathbb{Z}_{\ge0} }} - $({ A_p })_{ p = 5 }^{ 105 }\subseteq \mathbb{Z}_{\ge0}$
• {{MSeq|A_n|in=X|pre=\forall i\in\mathbb{N}\exists|post=[A_i<C]}} - $\forall i\in\mathbb{N}\exists ({ A_n })_{ n = 1 }^{ \infty }\subseteq X [A_i<C]$