Down Arrow in LaTeX (\downarrow)

Where it is used

Draws a downward arrow, used for decreasing limits, spin down, precipitates, and big-step reductions.

A sequence decreasing to its limit is written x_n \downarrow x, and one-sided limits appear as t \downarrow 0. Physicists write spin down as |\downarrow\rangle, and chemists put an arrow after a solid precipitate. In domain theory and programming language semantics, e\downarrow means a computation converges. Like \uparrow, it is a delimiter, so \Big\downarrow gives a taller arrow, handy in vertical diagram sketches. The double-shafted version is \Downarrow. Some topology and order-theory texts also write {\downarrow}x for the down-set of an element.

Also listed under: Chemistry

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Down Arrow: $\downarrow$

\[ \lim_{t \downarrow 0} \frac{f(x + t) - f(x)}{t} \]
\end{document}

Related symbols

• Left Arrow (Double)\Leftarrow
• Long Right Arrow\longrightarrow
• Right Arrow (Double)\Rightarrow
• Long Left Arrow\longleftarrow
• Up Arrow (Double)\Uparrow
• Up Arrow\uparrow

Frequently asked questions

How do I write Down Arrow in LaTeX?

Type \downarrow in math mode, for example $\lim_{t \downarrow 0} \frac{f(x + t) - f(x)}{t}$. It works in plain LaTeX without loading any package.

Which package do I need for \downarrow?

None. \downarrow is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \downarrow in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\downarrow$ in running text. If you only need the glyph in text, paste the Unicode character ↓ instead (with XeLaTeX or LuaLaTeX and a font that has it).