Similar or Equal in LaTeX (\simeq)

Where it is used

Tilde over a single line, read as homotopy equivalent, asymptotically equal or isomorphic.

Its meaning depends on the field: topologists write X \simeq Y for homotopy equivalence, category theorists for equivalence of categories, and physicists for approximate equality. Compare it with \cong (tilde over two lines), usually reserved for isomorphism or congruence, \approx (two tildes) for numerical approximation, and \sim for asymptotic equivalence or equivalence relations. Because the conventions overlap, state which one you use. As a relation symbol, it gets wide spacing on both sides automatically, so no manual spaces are needed.

Also listed under: Topology & Abstract Math

Minimal compilable example

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

\documentclass{article}
\begin{document}
Similar or Equal: $\simeq$

\[ S^n \setminus \{p\} \simeq \{\ast\} \]
\end{document}

Related symbols

• Arc\frown
• Similar To\sim
• Degree symbol^{\circ}
• Not Congruent\ncong
• Prime (feet/minutes)'
• Congruent\cong

Frequently asked questions

How do I write Similar or Equal in LaTeX?

Type \simeq in math mode, for example $S^n \setminus \{p\} \simeq \{\ast\}$. It works in plain LaTeX without loading any package.

Which package do I need for \simeq?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\simeq$ 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).