Template:MSeq
From Maths
Contents
Purpose
I very often have to write [ilmath](A_n)_{n=1}^\infty[/ilmath], and sometimes get lazy and just write [ilmath](A_n)[/ilmath] instead. To solve this I shall introduce this template:
- Template:MSeq - for "Mathematical sequence"
Caveats
- For [ilmath] ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] 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 [ilmath] ({ A_{n_j} })_{ j = 1 }^{ \infty } [/ilmath] this would be rendered as:
- {A_n}_{j}, yielding [ilmath]{A_n}_j[/ilmath] not [ilmath]A_{n_j} [/ilmath] (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 [ilmath] ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] is is A_n |
| 2 | index | n | The indexing variable, used for the "[ilmath]n[/ilmath]" in the "[ilmath]n=1[/ilmath]" part of [ilmath] ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] |
| 3 | from | 1 | The starting index of the sequence, eg the "1" in the "[ilmath]n=1[/ilmath]" part of [ilmath] ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] |
| 4 | to | \infty | The end index, eg the "[ilmath]\infty[/ilmath]" in [ilmath] ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] |
| (no index) | in | to say a "sequence in [ilmath]X[/ilmath]" means the sequence consists of elements of [ilmath]X[/ilmath], see abuses of the implies-subset relation for more. Represents the "[ilmath]\mathcal{X} [/ilmath]" in [ilmath] ({ A_n })_{ n = 1 }^{ \infty }\subseteq \mathcal{X} [/ilmath] | |
| (no index) | pre | Any math-markup preceding the sequence, eg the [ilmath]\exists[/ilmath] in [ilmath] \exists ({ A_n })_{ n = 1 }^{ \infty } [/ilmath] | |
| (no index) | post | Any math-markup after the sequence, eg the [ilmath][A_i<C][/ilmath] in [ilmath] \forall i\in\mathbb{N}\exists ({ A_n })_{ n = 1 }^{ \infty }\subseteq X [A_i<C] [/ilmath] |
Examples
- {{MSeq|A_k|k}} - [ilmath] ({ A_k })_{ k = 1 }^{ \infty } [/ilmath]
- {{MSeq|A_k|index=k}} - [ilmath] ({ A_k })_{ k = 1 }^{ \infty } [/ilmath]
- {{MSeq|A_p|p|5|105|in=\mathbb{Z}_{\ge0} }} - [ilmath] ({ A_p })_{ p = 5 }^{ 105 }\subseteq \mathbb{Z}_{\ge0} [/ilmath]
- {{MSeq|A_n|in=X|pre=\forall i\in\mathbb{N}\exists|post=[A_i<C]}} - [ilmath] \forall i\in\mathbb{N}\exists ({ A_n })_{ n = 1 }^{ \infty }\subseteq X [A_i<C] [/ilmath]
