# Notation: $g:2^{[2]}\rightarrow \mathbb{Z}$ what is $2^{[2]}$?

On Pg 28, Question 26 of this book, the author writes

Define $g:2^{[2]}\rightarrow \mathbb{Z}$ by the rule $g(S) = |S|$ where $S$ is any subset of $[2]$. Write $g$ as a set of ordered pairs.

I don't need the answers, just what it means.

-
Generally books tend to have a notation index at the end, where they keep all the notations they use, where they were defined and sometimes a two-words description. – Asaf Karagila Jul 28 '11 at 22:14

I assume that $[n]$ is the set of positive integers $\{ 1, 2, ... n \}$ and that for $S$ a set, $2^S$ is the set of all subsets of $S$. (The idea being that $|2^S| = 2^{|S|}$.)
I knew the notation for the power set but I hadn't seen $[n]$. Thanks. – kuch nahi Jul 28 '11 at 22:08
$[n]$ is defined on page 2. – Jonas Meyer Jul 28 '11 at 22:10
@kuch: then why didn't you ask "what is $[2]$"? – Qiaochu Yuan Jul 28 '11 at 22:12
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9730260968208313, "perplexity": 280.3037816131906}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701161718.0/warc/CC-MAIN-20160205193921-00043-ip-10-236-182-209.ec2.internal.warc.gz"}