Miscellaneous symbols

By “miscellaneous symbols” we mean the grab-bag of marks that belong to none of the Greek-letter, operator, relation, or arrow families yet turn up constantly in mathematics: analysis symbols such as infinity ∞, the partial sign ∂, and nabla ∇; the physics staples ℏ and ℓ; the geometry marks ∠ and △; the musical ♭ ♮ ♯; the ellipses … ⋯ for omissions; and the playing-card suits ♣ ♢ ♡ ♠. Most work in standard LaTeX, but a handful — \square, \circledR, the Hebrew \beth, and others — need the amssymb package. This page sorts out how to enter them, then gathers them into lookup tables grouped by use.

How to enter them, and the amssymb rule

Almost every symbol on this page is a command used inside math mode. Writing \infty straight into the body (text mode) is an error, so you enter math mode first, as in $\infty$. The exceptions are the text-mode marks: the section sign \S (§), the paragraph sign \P (¶), and \copyright (©) all work in ordinary text.

Next, the package rule. \infty, \partial, \nabla, \hbar, \ell, the various ellipses, the card suits, and more are available in standard LaTeX. By contrast, the white square \square (□), the measured angle \measuredangle (∡), the circled R \circledR (®), and Hebrew letters such as \beth (ℶ) are AMS additions that require \usepackage{amssymb} in the preamble. In the tables below, entries that need amssymb are flagged in the notes column.

\usepackage{amssymb}   % \square, \measuredangle, \circledR, \beth … に必要
% ...
体積 $V$ が $\infty$ に発散し、勾配は $\nabla f$ で表す。
\[ \frac{\partial f}{\partial x}, \qquad \angle ABC = 90^\circ, \qquad \triangle ABC \]

Analysis & calculus

The core symbols of analysis. All are standard LaTeX — no amssymb needed. Note that \prime (′) is rarely typed on its own; you normally use it as a superscript apostrophe for derivatives, f' (which equals f^{\prime}). And \surd (√) is only the “check” part of the radical sign — to actually set a square root, use the argument-taking \sqrt{...} instead.

Letter-like symbols (physics & math)

Symbols built from letters. The reduced Planck constant ℏ of quantum mechanics is \hbar; the script ell ℓ (for lengths, lines, or matrix eigenvalues) is \ell. The real- and imaginary-part symbols \Re and \Im output Fraktur ℜ and ℑ. To set an upright “Re” or “Im” as an operator instead, the modern choice is \operatorname{Re} / \operatorname{Im} from amsmath. Weierstrass’s p ℘ is \wp, and the infinite cardinal aleph ℵ is \aleph.

The Hebrew letters that follow aleph — beth ℶ, gimel ℷ, daleth ℸ — are used for cardinals in set theory, but they are undefined in standard LaTeX and **require amssymb** (\beth, \gimel, \daleth). Note that only \aleph itself is in the base set.

Geometry

Marks for angles and shapes. The angle \angle (∠) and triangle \triangle (△) are standard LaTeX. The measured angle \measuredangle (∡) and spherical angle \sphericalangle (∢), the white square \square (□) and black square \blacksquare (■), and the circled R \circledR (®) and circled S \circledS (Ⓢ) all **require amssymb**. The “□” that ends a proof (QED) is often \square too — and amsthm’s proof environment inserts it automatically.

A confusing pair is \Box (◻) and \Diamond (◇), the larger modal-logic symbols for “necessarily” and “possibly.” They require **latexsym or amssymb** (they are not in plain LaTeX) and are distinct from the AMS \square (□), with a different width.

Ellipses (dots)

The ellipses that stand in for omitted terms in sequences and matrices. All are standard LaTeX. Horizontally there are two: the baseline (low) \ldots (…) and the centered \cdots (⋯), and choosing the right one matters. Use the low \ldots in comma-separated lists, a_1, \ldots, a_n, and the centered \cdots between operators, a_1 + \cdots + a_n. The vertical \vdots (⋮) and diagonal \ddots (⋱) are the familiar ones in matrices.

If you would rather not decide, the generic \dots (…) is handy. In standard LaTeX it behaves like \ldots, but **once amsmath is loaded it looks at the context** and chooses automatically between low (e.g. before a comma) and centered (e.g. before an operator). For cases where the context cannot be inferred, amsmath also offers the explicit \dotsc (with commas), \dotsb (with binary operators), \dotsi (with integrals), and \dotso (other).

Musical symbols

The three accidentals are available in standard LaTeX: flat \flat (♭), natural \natural (♮), and sharp \sharp (♯). They are math-mode symbols, so wrap them in math when used in text, as in $\flat$ (write B\flat for B♭).

Card suits & other marks

The four card suits \clubsuit (♣), \diamondsuit (♢), \heartsuit (♡), and \spadesuit (♠) are all standard LaTeX math symbols (the outlined shapes; filled versions need amssymb or similar). The dagger \dagger (†) and double dagger \ddagger (‡), used for footnotes and notes, are standard too. These are math-mode commands, but the text-mode \dag and \ddag exist for use in the body.

As reference marks for body text, the section sign \S (§), the paragraph sign \P (¶, the pilcrow), and \copyright (©) work directly in text mode. Unlike the suits and daggers above, they do not need math mode.

Dotless i and j (for accents)

Finally, the dotless i and j for use with accents. Placing a hat or bar over i or j makes the original dot collide with the accent and look wrong. So you use the dot-removed \imath (ı) and \jmath (ȷ) as the base and add the accent on top, as in \hat{\imath} (the math î). This is the standard way to set the basis vectors î and ĵ.

% 点を取り除いてからアクセントを載せる
\[ \hat{\imath}, \quad \hat{\jmath}, \quad \vec{\imath} \]
% 比較: 点があるとアクセントとぶつかる
\[ \hat{i} \quad (\text{点とハットが重なる}) \]

Both \imath and \jmath are standard LaTeX; no amssymb needed. The empty set \emptyset (∅) and its rounded variant \varnothing (∅, which needs amssymb), together with the quantifiers \forall (∀) and \exists (∃) and other logic symbols, are covered together on the set & logic page.