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#### 16.2.5 Delimiters

Delimiters are parentheses, braces, or other characters used to mark the start and end of subformulas. This formula has three sets of parentheses delimiting the three subformulas.

(z-z_0)^2 = (x-x_0)^2 + (y-y_0)^2


The delimiters do not need to match, so you can enter $$[0,1)$$.

Here are the common delimiters:

DelimiterCommandName
((Left parenthesis
))Right parenthesis
\}{ or \lbraceLeft brace
\{} or \rbraceRight brace
[[ or \lbrackLeft bracket
]] or \rbrackRight bracket
\lfloorLeft floor bracket
\rfloorRight floor bracket
\lceilLeft ceiling bracket
\rceilRight ceiling bracket
\langleLeft angle bracket
\rangleRight angle bracket
//Slash, or forward slash
\\backslashReverse slash, or backslash
|| or \vertVertical bar
\| or \VertDouble vertical bar

The mathtools package allows you to create commands for paired delimiters. For instance, if you put \DeclarePairedDelimiter\abs{\lvert}{\rvert} in your preamble then you get two commands for single-line vertical bars (they only work in math mode). The starred version, such as \abs*{\frac{22}{7}}, has the height of the vertical bars match the height of the argument. The unstarred version, such as \abs{\frac{22}{7}}, has the bars fixed at a default height. This version accepts an optional argument, as in \abs[size command]{\frac{22}{7}}, where the height of the bars is given in size command, such as \Bigg. Using \lVert and \rVert as the symbols will give you a norm symbol with the same behavior.