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+\usepackage{amsmath}  % extensive math commands
+\usepackage{amsfonts} % more fonts for math (fracture, boldfaced and so on)
+\usepackage{mathtools} % extension to amsmath, with more sensible defaults (eq numbers only when referenced)
+\usepackage{amssymb} % more symbols, mostly redundant because already loaded by something else
+\usepackage{mathrsfs} % support for the RSFS fonts (through \mathscr command)
+\usepackage{cancel} % allows to cancel a part in math mode, for example to shorten a term
+\usepackage{bm} % bold mode in math, but better than \boldsymbol command from ams. \bm
+
+% number sets
+\NewDocumentCommand\N{}{\ensuremath{\mathbb{N}}}
+\NewDocumentCommand\R{}{\ensuremath{\mathbb{R}}}
+\NewDocumentCommand\Z{}{\ensuremath{\mathbb{Z}}}
+\NewDocumentCommand\Q{}{\ensuremath{\mathbb{Q}}}
+\NewDocumentCommand\C{}{\ensuremath{\mathbb{C}}}
+\NewDocumentCommand\O{}{\ensuremath{\emptyset}} % replaces the Ø
+
+% readable limits
+\let\svlim\lim{}
+\renewcommand\lim{\svlim\limits}
+
+% aliases
+\let\implies\Rightarrow{}
+\let\impliedby\Leftarrow{}
+
+\let\epsilon{\varepsilon} % I like the textual epsilon more