Prev: finite product
Next: Mathematicians on Facebook
From: Xah Lee on 27 Jun 2010 04:21
• Math Symbols in Unicode
http://xahlee.org/comp/unicode_math_operators.html

plain text version follows. The html version is much better because
the symbols are enlarged with css. And with working links.

---------------------------------------
Math Symbols in Unicode

Xah Lee, 2010-06-26

This page collects math symbols in Unicode.

Some Greeks: α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς τ υ φ χ ψ ω

superscript: ⁰ ⁱ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ⁿ

subscript: ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ ₐ ₑ ₒ ₓ ₔ

Roots: √ ∛ ∜

Sets: ℕ ℤ ℚ ℝ ℂ

Constants: ℯ ℵ ⅇ ⅈ ⅉ ∅ ∞ ⧜ ⧝ ⧞

Basic binary operators: × ÷ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊜ ⊝ ⊞ ⊟ ⊠ ⊡ − ∕ ∗ ∘ ∙ ⋅ ⋆

--------------------
Sets

element of: ∈ ∋ ∉ ∌ ⋶ ⋽ ⋲ ⋺ ⋳ ⋻

misc: ∊ ∍ ⋷ ⋾ ⋴ ⋼ ⋵ ⋸ ⋹ ⫙ ⟒

binary relation of sets: ⊂ ⊃ ⊆ ⊇ ⊈ ⊉ ⊊ ⊋ ⊄ ⊅ ⫅ ⫆ ⫋ ⫌ ⫃ ⫄ ⫇ ⫈ ⫉ ⫊ ⟃ ⟄ ⫏
⫐ ⫑ ⫒ ⫓ ⫔ ⫕ ⫖ ⫗ ⫘ ⋐ ⋑ ⟈ ⟉

Union: ∪ ⩁ ⩂ ⩅ ⩌ ⩏ ⩐

Intersection: ∩ ⩀ ⩃ ⩄ ⩍ ⩎

Binary operator on sets: ∖ ⩆ ⩇ ⩈ ⩉ ⩊ ⩋ ⪽ ⪾ ⪿ ⫀ ⫁ ⫂ ⋒ ⋓

N-nary operator on sets: ⋂ ⋃ ⊌ ⊍ ⊎

Joins: ⨝ ⟕ ⟖ ⟗

--------------------
Order

Precede and succeed: ≺ ≻ ≼ ≽ ≾ ≿ ⊀ ⊁ ⋞ ⋟ ⋠ ⋡ ⋨ ⋩ ⪯ ⪰ ⪱ ⪲ ⪳ ⪴ ⪵ ⪶ ⪷ ⪸ ⪹
⪺ ⪻ ⪼

less and greater: ≮ ≯ ≤ ≥ ≰ ≱ ⪇ ⪈ ≦ ≧ ≨ ≩

less and greater 2: ⋜ ⋝ ⪙ ⪚ ≶ ≷ ≸ ≹ ⋚ ⋛ ⪋ ⪌ ⪑ ⪒ ⪓ ⪔

with approx: ⪅ ⪆ ⪉ ⪊

less and greater with equivalence: ≲ ≳ ⋦ ⋧ ≴ ≵

less and greater with similarity: ⪝ ⪞ ⪟ ⪠ ⪍ ⪎ ⪏ ⪐

less and greater slanted: ⩽ ⩾ ⫹ ⫺ ⪕ ⪖ ⪛ ⪜

less and greater misc: ⪣ ⪤ ⪥ ⪦ ⪧ ⪨ ⪩ ⪪ ⪫ ⪬ ⪭ ⪮ ⪡ ⪢ ⫷ ⫸ ⩹ ⩺ ⩻ ⩼ ≬ ≪ ≫ ⋘
⋙

Order relation with dot: ⋖ ⋗ ⩿ ⪀ ⪗ ⪘ ⪁ ⪂ ⪃ ⪄

--------------------
Equality, Identity, Equivalence, Approx, Congruence

equality: ≝ ≞ ≟ ≠ ∹ ≎ ≏ ≐ ≑ ≒ ≓ ≔ ≕ ≖ ≗ ≘ ≙ ≚ ≛ ≜ ⩬ ⩭ ⩮ ⩱ ⩲ ⩦ ⩴ ⩵ ⩶ ⩷

Identity: ≡ ≢ ⩧

Equivalence: ≍ ≭ ≣ ⩸

Approx equality: ≁ ≂ ≃ ≄ ⋍ ≅ ≆ ≇ ≈ ≉ ≊ ≋ ≌ ⩯ ⩰

Misc equality: ∻

Misc relations: ⊏ ⊐ ⊑ ⊒ ⊓ ⊔ ⋢ ⋣ ⋤ ⋥ ⊲ ⊳ ⊴ ⊵ ⋪ ⋫ ⋬ ⋭ ⫴ ⫵

--------------------
Logic

Logic: ¬ ⫬ ⫭ ⊨ ⊭ ∀ ∁ ∃ ∄ ∴ ∵ ⊦ ⊬ ⊧ ⊩ ⊮ ⊫ ⊯ ⊪ ⊰ ⊱

Logic binary: ∧ ∨ ⊻ ⊼ ⊽ ⋎ ⋏ ⟑ ⟇ ⩑ ⩒ ⩓ ⩔ ⩕ ⩖ ⩗ ⩘ ⩙ ⩚ ⩛ ⩜ ⩝ ⩞ ⩟ ⩠ ⩢ ⩣ ⨇
⨈

Logic n-nary: ⋀ ⋁

n-nary operators: ∑ ⨀ ⨁ ⨂ ⨃ ⨄ ⨅ ⨆ ∏ ∐ ∔

--------------------
Geometry

Geometry: ∣ ∤ ⫮ ⌅ ⌆ ℓ ⫛

Ratio and proportion: ∝ ∶ ∷ ∺

Parallel and perpendicular: ∥ ∦ ⫲ ⫳ ⋕ ⟂ ⫡

Right angle: ∟ ⊾ ⦜ ⦝ ⊿

Angles: ∠ ∡ ⦛ ⦞ ⦟ ⦢ ⦣ ⦤ ⦥ ⦦ ⦧ ⦨ ⦩ ⦪ ⦫ ⦬ ⦭ ⦮ ⦯ ⦓ ⦔ ⦕ ⦖ ⟀

Spherical angle: ∢ ⦠ ⦡

--------------------
...

Pairs: ⌈ ⌉ ⌊ ⌋ ⦋ ⦌ ⟦ ⟧ ⦍ ⦎ ⦏ ⦐

pairs 2: ⟮ ⟯ ⟨ ⟩ ⟪ ⟫ ⦃ ⦄ ⦅ ⦆ ⦇ ⦈ ⦉ ⦊ ⟬ ⟭ ⦗ ⦘ ⦑ ⦒ ⧼ ⧽

integrals: ∫ ∬ ∭ ∮ ∯ ∰ ∱ ∲ ∳ ⨋ ⨌ ⨍ ⨎ ⨏ ⨐ ⨑ ⨒ ⨓ ⨔ ⨕ ⨖ ⨗ ⨘ ⨙ ⨚ ⨛ ⨜

Derivative: ∂ ′ ″ ‴ ∆

vector: ⨯ ∇ ⊹

Misc indicators: ∎ ± ∓ ⋮ ⋯ ⋰ ⋱

Misc symbols: ∿

Tacks: ⊣ ⊢ ⊥ ⊤ ⟘ ⟙ ⟛ ⟝ ⟞ ⟟ ⫧ ⫨ ⫩ ⫪ ⫫ ⫞ ⫟ ⫠

Turnstiles: ⫢ ⫣ ⫤ ⫥ ⟚

Z notation: ⦁ ⦂ ⩤ ⩥ ⨟ ⨠ ⨡ ⨾

Tilde Operators: ∼ ∽ ⩪ ⩫ ⩳

Misc Operators: ⋄ ⫶ ⫼ ⫾

Misc products: ≀ ⨿ ⨼ ⨽ ⧢ ⋉ ⋊ ⋋ ⋌

Plus variations: ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨭ ⨮

Solidus: ⫻ ⫽

minus sign variations: ∸ ⨩ ⨪ ⨫ ⨬

maps: ⊶ ⊷ ⊸ ⟜ ⧟

Unsorted: ∾ ⊺ ⋇ ⟌ ⟠ ⋔ ⫚ ⋈ ⟁ ⟅ ⟆ ⟊ ⟐ ⟓ ⟔ ⟡ ⟢ ⟣ ⟤ ⟥ ⦀ ⦙ ⦚ ⧘ ⧙ ⧚ ⧛ ⦰ ⦱ ⦲
⦳ ⦴ ⦵ ⦶ ⦷ ⦸ ⦹ ⦺ ⦻ ⦼ ⦽ ⦾ ⦿ ⧀ ⧁ ⧂ ⧃ ⧄ ⧅ ⧆ ⧇ ⧈ ⧉ ⧑ ⧒ ⧓ ⧔ ⧕ ⧖ ⧗ ⧠ ⧡ ⧣ ⧤ ⧥
⧦ ⧧ ⧨ ⧩ ⧪ ⧫ ⧬ ⧭ ⧮ ⧯ ⧰ ⧱ ⧲ ⧳ ⧴ ⧵ ⧶ ⧷ ⧸ ⧹ ⧺ ⧻ ⧾ ⨉ ⨊ ⨞ ⧊ ⧋ ⧌ ⧍ ⨹ ⨺ ⨻ ⧎ ⧏
⧐ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⩡ ⩨ ⩩ ⫍ ⫎ ⫝̸ ⫝ ⫦ ⫯ ⫰ ⫱

--------------------
What Chars Are Included

These are roughly “all” math related symbols under the Basic
Multilingual Plane (BMP). The total number of chars on this page is
about 766.

For few hundred arrows, see: Arrows in Unicode. There are also a few
hundred drawing shapes, used together for example to tile into a large
braket or boxes, corner, for matrixes, etc. You can see them here:
unicode_shapes.txt. There are also few hundred dingbats in unicode,
some could be used for math, but are not considered math symbols here.

There are more math symbols but are outside of BMP, and i'm not aware
of any fonts that shows much of chars outside BMP. In particular,
there are several set of specially rendered alphabets, such as double
struck capital letters, Fraktur (aka gothic), bold slanted... They are
outside of BMP. You can see them here: unicode_math_alphanum.txt. You
can see also part of the operator set grouped by code point, here:
unicode_math_operators.txt

Note: this page will be improved over the coming months. e.g. The
bunch of less used misc symbols at the bottom can still use some
categorizing.

--------------------
I See Blank Squares?

If some shows up as square, that's probably because you don't have the
right font, or your browser is old and isn't configured properly, or
your browser simply does not work well. Exact reason can be complex.
As of 2010-06-27, latest versions of the following browsers on Windows
Vista show all characters (assuming you have the right font first):
Google Chrome, Opera, Firefox.

To get proper fonts, see: Best Unicode Fonts.

To find out the unicode name and code point of the char, use emacs.
See: xub Unicode Browser mode for Emacs.

--------------------
Unicode Names for Symbol's Meaning

The symbols are roughly grouped by purpose, and with respect to the
symbol's semantic meaning, as opposed to their appearance.

For example, there are many similar looking symbols, and in different
fonts they may look different or identical. e.g. ~ ∼ ∿ ∽ ≈. The first
is “tilde”, the second is “tilde operator”, third is “sine wave”, 4th
is “reversed tilde”, 5th is “almost equal to”.

Another example: ⩳ ≌ ⩯ ⩰. Their names are:

* ⩳ EQUALS SIGN ABOVE TILDE OPERATOR
* ≌ ALL EQUAL TO
* ⩯ ALMOST EQUAL TO WITH CIRCUMFLEX ACCENT
* â©° APPROXIMATELY EQUAL OR EQUAL TO

The unicode names give indication of the symbol's meaning. There are
some 20 more symbols that's made up wavy line(s) and or horizontal
line(s). Best to go by the symbol's name in your choice a symbol,
because what you see as rendered by a font may be very different from
another font, and often font designers simply got the shape wrong,
especially for less common chars.

--------------------
Formal Language, not Glyphs with no Grammar

Also, i've organized these symbols with respect to their use in
calculational proof and formal language. e.g. use in computer proof
languages (e.g. Hol, Coq, Isabelle, OCaml) or computer algebra systems
(e.g. Mathematica). The symbol's meaning are precisely defined and
parsed by a compiler. This is in contrast to traditional math (e.g.
LaTeX) where the symbols serve as a picture for communication with
humans. See:

* Math Notations, Computer Languages, and the “Form” in Formalism
* The Problems of Traditional Math Notation

Xah
∑ http://xahlee.org/

☄
From: Henry on 28 Jun 2010 14:09
On 27 June, 09:21, Xah Lee <xah...(a)gmail.com> wrote:
> • Math Symbols in Unicode
> plain text version follows. The html version is much better because
> the symbols are enlarged with css. And with working links.

It is not a good idea to post such things to a news group,
as for most people many of the characters are unreadable here
and many of them still unreadable in html.

pdf has fewer problems, such as the symbols in
http://www.unicode.org/charts/PDF/U2A00.pdf

From: Xah Lee on 28 Jun 2010 14:20
On Jun 28, 11:09 am, Henry <s...(a)btinternet.com> wrote:
> On 27 June, 09:21, Xah Lee <xah...(a)gmail.com> wrote:
>
> > • Math Symbols in Unicode
> > http://xahlee.org/comp/unicode_math_operators.html
> > plain text version follows. The html version is much better because
> > the symbols are enlarged with css. And with working links.
>
> It is not a good idea to post such things to a news group,
> as for most people many of the characters are unreadable here
> and many of them still unreadable in html.
>
> pdf has fewer problems, such as the symbols in http://www.unicode.org/charts/PDF/U2A00.pdf

if you have the right fonts installed, then all the chars on that page
shows in latest versions of Google Chrome, Firefox, Opera.

they all show in emacs, of course.

you can find the best fonts for unicode here:

• Best Fonts for Unicode
http://xahlee.org/emacs/emacs_unicode_fonts.html

proper font is critical if you need to use these symbols anyway.

The problem of showing all unicode by a table as in the unicode
document is that, the math symbols are scattered all over the
different sections. Let's say you work in logic, and needed some
symbols commonly found in logic field. It's basically impossible to
find them in any convenient way using just about any unicode
references, including Mac's character palette or Windows's charmap.

what is better needed is a collection of the symbols by purpose.

for example, you needed to see all symbols provided in unicode related
to say the Union and intersection operators.

That is why i created the page.

The Mac's Character Palette somewhat also addressed this practical
need, by letting you view all math symbols in one pane of the
interface. But it is general for public users, not finely grouped for
professional use.

Xah
∑ http://xahlee.org/

☄
From: Norbert_Paul on 29 Jun 2010 02:35
Henry wrote:
> On 27 June, 09:21, Xah Lee<xah...(a)gmail.com> wrote:
> It is not a good idea to post such things to a news group,
It is not a good idea to read Xah Lee's posts, either.
From: Marc Mientki on 29 Jun 2010 03:25
Am 28.06.2010 20:20, schrieb Xah Lee:

> if you have the right fonts installed, then all the chars on that page
> shows in latest versions of Google Chrome, Firefox, Opera.
>
> they all show in emacs, of course.

Not in my Emacs (23.2.1 on windows XP)

Sorry, but slowly I find your posts as spam. Many of your
proposals look strange for me. This starts with your indentation
and typography of Lisp codes and use of CamelCase, and ends
with your very strange criticism of fundamental values of Emacs.


regards
Marc


 |  Next  |  Last
Pages: 1 2
Prev: finite product
Next: Mathematicians on Facebook