Divides / such that (∣) in LaTeX
\mid produces a single vertical bar (∣) used as a relation, most commonly for 'divides' in number theory and for 'such that' inside set-builder notation.
LaTeX command
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In number theory, means a divides b exactly, that is, b is an integer multiple of a. This is a statement about integers, entirely different from a fraction: is true, while 2/6 is a number. The negation is \nmid, giving .
Inside curly braces, \mid reads as 'such that': \{ > 0\} is the set of all x satisfying the condition after the bar. \mid is also the standard way to write the bar in conditional probability, P(), where it gets sensible spacing that a plain typed pipe does not.
\mid is a relation, so avoid it where you actually want a delimiter. Absolute value bars should be \lvert x \rvert (or plain | for quick notes), and a function restriction uses a bare bar with a subscript, f|_A, rather than \mid.
Other forms
\nmiddoes not divide (∤)Examples
$2 \mid 6$2 divides 6
$\{x \mid x > 0\}$set-builder notation, read as 'such that'
$P(A \mid B)$conditional probability, correctly spaced
$7 \nmid 15$7 does not divide 15
Tips and common mistakes
- Use
\mid, not a plain typed |, inside set-builder notation and conditional probability; the spacing is noticeably better in both directions. - For 'does not divide', use
\nmidrather than typing\midwith a slash on top; it needs the amssymb package. - If the set on either side of \{ \} needs to grow, wrap the braces in
\left\{...\right\}, and\midwill usually still sit correctly in the middle. - Don't reuse
\midfor absolute value bars; use\lvertx\rvertinstead, which pairs correctly and matches how mathematicians expect a delimiter to behave.
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What's the difference between \mid and | in LaTeX?
\mid is a relation with built-in spacing, suited to 'divides' and 'such that'. A plain | is just a character, commonly used as a quick absolute value delimiter but with no spacing logic of its own.
How do I write 'such that' in set notation?
Put \mid inside the braces: \{(x)\} reads as 'the set of x such that P(x) holds'.
How do I write 'does not divide' in LaTeX?
Use \nmid, which renders as ∤ and requires the amssymb package.
Should I use \mid for conditional probability?
Yes, P() is the standard, well-spaced way to typeset it, better than a plain vertical bar character.