Appendix G — Notation

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Last modified: 2024-05-16: 18:35:36 (PM)

Table G.1: Notation used in this book

symbol	meaning	LaTeX
\(\neg\)	not	`\neg`
\(\forall\)	all	`\forall`
\(\exists\)	some	`\exists`
\(\cup\)	union, “or”	`\cup`
\(\cap\)	intersection, “and”	`\cap`
\(\mid\)	given, conditional on	`\mid`, `\|`
\(\sum\)	sum	`\sum`
\(\prod\)	product	`\prod`
\(\mu\)	mean	`\mu`
\(\mathbb{E}\)	expectation	`\mathbb{E}`
\('\)	transpose or derivative¹	`'`
\(⫫\)	independent	`⫫`
\(\therefore\)	therefore, thus	`\therefore`
\(\eta\)	linear component of a GLM	`eta`

The percent sign “%” is just a shorthand for “\(\times \frac{1}{100}\)”. The word “percent” comes from the Latin “per centum”; “centum” means 100 in Latin, so “percent” means “per hundred” (c.f., https://en.wikipedia.org/wiki/Percentage)

So, contrary to what you may have learned previously, \(10\% = 0.1\) is a true and correct equality.

Proof. \[ \begin{aligned} 10\% &= 10 \times \frac{1}{100} \\ &= \frac{10}{100} \\ &= 0.1 \end{aligned} \]

depending on whether it is applied to a matrix or a function ## The percent sign↩︎

# Notation

{{< include macros.qmd >}}

| symbol | meaning | LaTeX
|-----------|---------|-----------
| $\neg$    | not                                            | `\neg`
| $\forall$ | all                                            | `\forall`
| $\exists$ | some                                           | `\exists`
| $\cup$    | union, "or"                                    | `\cup`
| $\cap$    | intersection, "and"                            | `\cap`
| $\mid$    | given, conditional on                          | `\mid`, `|`
| $\sum$    | sum                                            | `\sum`
| $\prod$   | product                                        | `\prod`
| $\mu$     | mean                                           | `\mu`
| $\Expp$   | [expectation](probability.qmd#def-expectation) | `\mathbb{E}`
| $'$       | transpose or derivative[^1]                    | `'`
| $\ind$    | [independent](probability.qmd#def-indpt)       | `⫫`
| $\tf$     | therefore, thus                                | `\therefore`
| $\eta$    | [linear component of a GLM][eta]               | `eta`

: Notation used in this book {#tbl-notation-collected}

[eta]: https://en.wikipedia.org/wiki/Generalized_linear_model#:~:text=The%20linear%20predictor%20is%20the,data%20through%20the%20link%20function "linear predictor notation"

[^1]: depending on whether it is applied to a matrix or a function
## The percent sign

The percent sign "%" is just a shorthand for "$\times \frac{1}{100}$". 
The word "percent" comes from the Latin "per centum"; "centum" means 100 in Latin, so "percent" means "per hundred" (c.f., <https://en.wikipedia.org/wiki/Percentage>)

So, contrary to what you may have learned previously, $10\% = 0.1$ is a true and correct equality.

:::{.proof}

$$
\ba
10\% &= 10 \times \frac{1}{100}
\\ &= \frac{10}{100}
\\ &= 0.1
\ea
$$

:::