math symbols in unicode collection
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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 Ï Ï Ï Ï Ï Ï Ï Ï Ï superscript: ⰠⱠ² ³ ⴠⵠⶠⷠ⸠⹠⺠⻠⼠⽠⾠⿠subscript: â â â â â â â â â â â â â â â â â â â â Roots: â â â Sets: â ⤠â â â Constants: ⯠ⵠâ â â â â ⧠⧠⧠Basic binary operators: à ÷ â â â â â â â â â â â â â¡ â â â â â â â -------------------- Sets element of: â â â â ⶠ⽠Ⲡ⺠Ⳡ⻠misc: â â ⷠ⾠ⴠ⼠ⵠ⸠⹠⫠â binary relation of sets: â â â â â â â â â â â« â« â« â« â« â« â« â« â« â« â â â« â« â« â« â« â« â« â« â« â« â â â â Union: ⪠⩠⩠⩠⩠⩠⩠Intersection: â© â© â© â© â© â© Binary operator on sets: â ⩠⩠⩠⩠⩠⩠⪽ ⪾ ⪿ â« â« â« â â N-nary operator on sets: â â â â â Joins: ⨠â â â -------------------- Order Precede and succeed: ⺠⻠⼠⽠⾠⿠â â â â â ⡠⨠⩠⪯ ⪰ ⪱ ⪲ ⪳ ⪴ ⪵ ⪶ ⪷ ⪸ ⪹ ⪺ ⪻ ⪼ less and greater: ⮠⯠⤠⥠ⰠⱠ⪠⪠⦠⧠⨠⩠less and greater 2: â â ⪠⪠ⶠⷠ⸠⹠â â ⪠⪠⪠⪠⪠⪠with approx: ⪠⪠⪠⪠less and greater with equivalence: ⲠⳠ⦠⧠ⴠⵠless and greater with similarity: ⪠⪠⪠⪠⪠⪠⪠⪠less and greater slanted: ⩽ ⩾ ⫹ ⫺ ⪠⪠⪠⪠less and greater misc: ⪣ ⪤ ⪥ ⪦ ⪧ ⪨ ⪩ ⪪ ⪫ ⪬ ⪠⪮ ⪡ ⪢ â«· ⫸ ⩹ ⩺ â©» ⩼ ⬠⪠⫠â â Order relation with dot: â â â©¿ ⪠⪠⪠⪠⪠⪠⪠-------------------- Equality, Identity, Equivalence, Approx, Congruence equality: â â â â â¹ â â â â â â â â â â â â â â â ⩬ â© â©® ⩱ ⩲ ⩦ â©´ ⩵ ⩶ â©· Identity: ⡠⢠⩧ Equivalence: â â ⣠⩸ Approx equality: â â â â â â â â â â â â â ⩯ â©° Misc equality: â» Misc relations: â â â â â â ⢠⣠⤠⥠ⲠⳠⴠⵠ⪠⫠⬠â â«´ ⫵ -------------------- Logic Logic: ¬ ⫬ ⫠⨠â â â â â ⴠⵠ⦠⬠⧠⩠⮠⫠⯠⪠ⰠⱠLogic binary: ⧠⨠⻠⼠⽠â â â â â© â© â© â© â© â© â© â© â© â© â© â© â© â© â© â© â©¢ â©£ ⨠⨠Logic n-nary: â â n-nary operators: â ⨠⨠⨠⨠⨠⨠⨠â â â -------------------- Geometry Geometry: ⣠⤠⫮ â â â â« Ratio and proportion: â ⶠⷠ⺠Parallel and perpendicular: ⥠⦠⫲ ⫳ â â â«¡ Right angle: â ⾠⦠⦠⿠Angles: â ⡠⦠⦠⦠⦢ ⦣ ⦤ ⦥ ⦦ ⦧ ⦨ ⦩ ⦪ ⦫ ⦬ ⦠⦮ ⦯ ⦠⦠⦠⦠â Spherical angle: ⢠⦠⦡ -------------------- ... Pairs: â â â â ⦠⦠⦠⧠⦠⦠⦠⦠pairs 2: ⮠⯠⨠⩠⪠⫠⦠⦠⦠⦠⦠⦠⦠⦠⬠â ⦠⦠⦠⦠⧼ ⧽ integrals: ⫠⬠â ⮠⯠ⰠⱠⲠⳠ⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠⨠Derivative: â â² â³ â´ â vector: ⨯ â â¹ Misc indicators: â ± â ⮠⯠ⰠⱠMisc symbols: â¿ Tacks: ⣠⢠⥠⤠â â â â â â ⫧ ⫨ â«© ⫪ â«« â« â« â« Turnstiles: â«¢ â«£ ⫤ â«¥ â Z notation: ⦠⦠⩤ â©¥ ⨠⨠⨡ ⨾ Tilde Operators: ⼠⽠⩪ â©« ⩳ Misc Operators: â ⫶ ⫼ ⫾ Misc products: â ⨿ ⨼ ⨽ ⧢ â â â â Plus variations: ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨠⨮ Solidus: â«» ⫽ minus sign variations: ⸠⨩ ⨪ ⨫ ⨬ maps: ⶠⷠ⸠â ⧠Unsorted: ⾠⺠â â â â â« â â â â â â â â ⡠⢠⣠⤠⥠⦠⦠⦠⧠⧠⧠⧠⦰ ⦱ ⦲ ⦳ ⦴ ⦵ ⦶ ⦷ ⦸ ⦹ ⦺ ⦻ ⦼ ⦽ ⦾ ⦿ ⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧠⧡ ⧣ ⧤ ⧥ ⧦ ⧧ ⧨ ⧩ ⧪ ⧫ ⧬ ⧠⧮ ⧯ ⧰ ⧱ ⧲ ⧳ ⧴ ⧵ ⧶ ⧷ ⧸ ⧹ ⧺ ⧻ ⧾ ⨠⨠⨠⧠⧠⧠⧠⨹ ⨺ ⨻ ⧠⧠⧠⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ â©¡ ⩨ â©© â« â« â«Ì¸ ⫠⫦ ⫯ â«° ⫱ -------------------- What Chars Are Included These are roughly âallâ 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. ~ â¼ â¿ â½ â. The first is âtildeâ, the second is âtilde operatorâ, third is âsine waveâ, 4th is âreversed tildeâ, 5th is âalmost equal toâ. Another example: ⩳ â ⩯ â©°. Their names are: * ⩳ EQUALS SIGN ABOVE TILDE OPERATOR * â 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 âFormâ in Formalism * The Problems of Traditional Math Notation Xah â http://xahlee.org/ â
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 â http://xahlee.org/ â
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 |