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B018-622300-451485Table of Braille Mathematical Signs with Unicode ReferencesDisclaimerThis guidance may include references to external websites, services or products for which UKAAF accepts no responsibility. This information is given without any representation or endorsement of those websites, services or products.Copyright ? 2019 UK Association for Accessible Formats (UKAAF). Not for re-sale. You may reproduce in whole or in part with acknowledgement to UKAAF.Contents TOC \o "1-2" \h \z \u Introduction PAGEREF _Toc517355373 \h 3Braille Indicators PAGEREF _Toc517355374 \h 3Comparison Signs PAGEREF _Toc517355375 \h 5Operation Signs PAGEREF _Toc517355376 \h 7Brackets PAGEREF _Toc517355377 \h 8Greek Letters PAGEREF _Toc517355378 \h 9Miscellaneous PAGEREF _Toc517355379 \h 11Embellishments PAGEREF _Toc517355380 \h 14Arrows PAGEREF _Toc517355381 \h 15Shapes PAGEREF _Toc517355382 \h 18Transcriber Defined Signs PAGEREF _Toc517355383 \h 19UK Association for Accessible Formats (UKAAF) PAGEREF _Toc517355384 \h 21Contact details PAGEREF _Toc517355385 \h 21Registered address PAGEREF _Toc517355386 \h 21Further Information PAGEREF _Toc517355387 \h 21IntroductionThe following is a summary of mathematical signs in UEB. Unicode numbers and descriptions are given where available.Note, a number of UEB symbols in the tables below must be shown in grade 1 mode. Grade 1 indicators are not shown in the following tables, but may be needed in practical use. Simplistically, if a sign also has a grade 2 contracted meaning, then it needs to be in grade 1 mode to have its mathematical meaning. For information on the placement of grade 1 indicators, see Guidelines for Mathematics, available from braille/ueb. For more information on UEB generally, see Rules of Unified English Braille, and Guidelines for Technical Material, latest edition, available from ueb.The braille signs in the following tables should generally be used to represent the corresponding print signs whatever their meaning.Braille IndicatorsThese signs are used as part of the braille code, they have no direct print equivalent.BrailleDescription#Numeric indicator##Numeric passage indicator#'Numeric passage terminator/Simple numeric fraction line(General fraction open indicator./General fraction line)General fraction close indicator9Superscript indicator5Subscript indicator.9Directly above.5Directly below%Open radical (root)+Close radical (root)<Opening braille grouping indicator>Closing braille grouping indicator"Line continuation indicator""Line continuation indicator with space;Grade 1 symbol indicator;;Grade 1 word indicator;;;Grade 1 passage indicator;'Grade 1 terminator,Capital letter indicator,,Capital word indicator,,,Capital passage indicator,'Capital terminator^1Bold word indicator^2Bold symbol indicator^7Bold passage indicator^'Bold terminator@1Script word indicator@2Script symbol indicator@7Script passage indicator@'Script terminatorComparison SignsThese are normally spaced on both sides.PrintBrailleUnicodeDescription="7003DEquals≠"7@:2260Not equal<@<003CLess than≤_@<2264Less than or equal to>@>003EGreater than≥_@>2265Greater than or equal to?.@<226AMuch less than?.@>226BMuch greater than≮@<@:226ENot less than≯@>@:226FNot greater than?_@<@:2270Neither less than nor equal to?_@>@:2271Neither greater than nor equal to∝_"7221DProportional to?_92243Approximately equal to (tilde over horizontal line)?"_92245Approximately equal to (tilde over equals sign)≈^92248Approximately equal (tilde over tilde)?^"7224FEquals with bump in top bar (difference between)?."72251Geometrically equal to (equals dotted above and below)≡_=2261Equivalent to (three horizontal lines)?_=@:2262Not identical to∈^e2208Element of (member of)?^e@:2209Not an element of?@^e220BContains as member?@^e@:220CDoes not contain as member?^<2282Subset of (is contained in)?^>2283Superset (contains)?^<@:2284Not a subset of?^>@:2285Not a superset of?_^<2286Subset or equal to?_^>2287Superset or equal to?_^<@:2288Neither subset nor equal to?_^>@:2289Neither superset nor equal to?.^<228ASubset but not equal to?.^>228BSuperset but not equal to?@_<22B2Normal subgroup of?@_>22B3Contains as normal subgroup?__<22B4Normal subgroup of or equal to?__>22B5Contains as normal subgroup of or equal to?#_l2AF4Triple vertical barOperation SignsThese signs are generally not spaced.PrintBrailleUnicodeDescription+"6002BPlus sign?"-2212Minus sign×"800D7Multiplication sign (times)÷"/00F7Division sign (divided by)±_600B1Plus or minus?_-2213Minus or plus?"92217Asterisk operator°"02218Ring operator～@9223CTilde operator?"422C5Dot operator∧@82227Logical and∨@62228Logical or∩.82229Intersection∪.6222AUnion?_*2216Set minusBracketsBrackets are usually unspaced. The multiline brackets are used when a print bracket spans more than one line of text (e.g. for vectors and matrices) and must be vertically aligned in the braille.PrintBrailleUnicodeDescription("<0028Left parenthesis)">0029Right parenthesis[.<005BLeft square bracket].>005DRight square bracket{_<007BLeft curly bracket}_>007DRight curly bracket?@<2329Left angle bracket?@>232ARight angle bracket|_\007CVertical bar,"<Multiline left parenthesis,">Multiline right parenthesis,.<Multiline left square bracket,.>Multiline right square bracket,_<Multiline left curly bracket,_>Multiline right curly bracket,_\Multiline vertical barGreek LettersGreek letters may be used as needed. Some Greek letters have variant visual forms.PrintBrailleUnicodeDescriptionα.a03B1Greek alphaβ.b03B2Greek betaγ.g03B3Greek gammaδ.d03B4Greek deltaε.e03B5Greek epsilonζ.z03B6Greek zetaη.:03B7Greek etaθ.?03B8Greek thetaι.i03B9Greek iotaκ.k03BAGreek kappaλ.l03BBGreek lambdaμ.m03BCGreek muν.n03BDGreek nuξ.x03BEGreek xiο.o03BFGreek omicronπ.p03C0Greek piρ.r03C1Greek rhoσ.s03C3Greek sigmaτ.t03C4Greek tauυ.u03C5Greek upsilonφ.f03C6Greek phiχ.&03C7Greek chiψ.y03C8Greek psiω.w03C9Greek omegaNote that several of the uppercase Greek letters look very similar to Latin capital letters.PrintBrailleUnicodeDescriptionΑ,.a0391Capital Greek alphaΒ,.b0392Capital Greek betaΓ,.g0393Capital Greek gammaΔ,.d0394Capital Greek deltaΕ,.e0395Capital Greek epsilonΖ,.z0396Capital Greek zetaΗ,.:0397Capital Greek etaΘ,.?0398Capital Greek thetaΙ,.i0399Capital Greek iotaΚ,.k039ACapital Greek kappaΛ,.l039BCapital Greek lambdaΜ,.m039CCapital Greek muΝ,.n039DCapital Greek nuΞ,.x039ECapital Greek xiΟ,.o039FCapital Greek omicronΠ,.p03A0Capital Greek piΡ,.r03A1Capital Greek rhoΣ,.s03A3Capital Greek sigmaΤ,.t03A4Capital Greek tauΥ,.u03A5Capital Greek upsilonΦ,.f03A6Capital Greek phiΧ,.&03A7Capital Greek chiΨ,.y03A8Capital Greek psiΩ,.w03A9Capital Greek omegaNote also the following:PrintBrailleUnicodeDescription?.m00B5Micro (Greek mu)?,.w2126Ohm sign (capital Greek omega)?,.d2206Increment (capital Greek delta)∏,.p220FProduct (capital Greek pi)∑,.s2211Sum (capital Greek sigma)MiscellaneousPrintBrailleUnicodeDescription +Visible space!60021Exclamation (factorial)#_?0023Number sign (hash)%.00025Percent sign&@&0026Ampersand*"9002AAsterisk,1002Ccomma--002DHyphen.4002EFull stop (decimal point)/_/002FSolidus (slash):3003AColon;2003BSemicolon?8003FQuestion mark@@a0040Commercial at sign\_*005CBackslash^@5005ECaret (hat, up arrow)_.-005FLow line (underscore)~@9007ETilde (swung dash)?@c00A2Cents sign€@e20ACEuro sign?@f20A3French franc sign?@l00A3Pound sign?@n20A6Naira sign$@s0024Dollar sign?@y00A5Yen sign?.\00A6Broken bar?@?00ACNot sign°^j00B0Degree sign?@,?2020Dagger?@,]2021Double dagger…4442026Ellipsis′72032Prime sign″772033Double prime sign?7772034Triple prime sign?,^$a212BAngstrom symbol?^a2200For all?@d2202Partial differential?^52203There exists?^5@:2204There does not exist?@j2205Empty set?^d2207Nabla (del, inverted capital delta)?_$#d220EEnd of proof√"%221ASquare root (radical) without vinculum∞#=221EInfinity∠_[2220Angle?._[2221Measured angle?#_[22BERight angle with arc∫!222BIntegral∮@!222EContour integral (closed line integral)∴,*2234Therefore∵@/2235Because (since)∶32236Ratio∷332237Proportion∣_\2223Divides?_\@:2224Does not divide∥#l2225Parallel?#l@:2226Not parallel?#-27C2Perpendicular⊥#-22A5Up tack (perpendicular)?_322A6Assertion (is a theorem)?@_322A3Left tack (reverse assertion)?^_322A8True (is valid)?_3@:22ACDoes not prove?^_3@:22ADNot true?._32AE4Vertical bar double left turnstile?@%2713Check mark (tick)?.j29B5Plimsoll sign (standard state)EmbellishmentsEmbellishments may be applied after a symbol. They apply to the previous "item", as defined in the Rules of Unified English Braille.BrailleDescription:Bar over previous item@:Line through previous item (cancellation)^:Simple right arrow over previous item_:Tilde over previous item":Hat over previous item._:Arc over previous item^4Dot over previous item,:Bar under previous item,^:Simple right arrow under previous item,_:Tilde under previous item,":Hat under previous item,^4Dot under previous itemArrowsMany arrows may be constructed in UEB. A selection is shown below. Note that most arrows begin with the arrow indicator \, or the bold arrow indicator ^\.PrintBrailleUnicodeDescription←\[2190Leftwards arrow↑\+2191Upwards arrow→\o2192Rightwards arrow↓\%2193Downwards arrow?\wro2194Left right arrow?\wr+2195Up down arrow↖\:2196Northwest arrow↗\s2197Northeast arrow↘\<2198Southeast arrow↙\>2199Southwest arrow?\[@:219ALeftwards arrow with stroke?\o@:219BRightwards arrow with stroke?\95[219CLeftwards wave arrow?\59o219DRightwards wave arrow?\3rr[219ELeftwards two headed arrow?\3rr+219FUpwards two headed arrow?\3rro21A0Rightwards two headed arrow?\3rr%21A1Downwards two headed arrow?\rr[21A2Leftwards arrow with tail?\rro21A3Rightwards arrow with tail?\\r[21A4Leftwards arrow from bar?\\r+21A5Upwards arrow from bar?\|ro21A6Rightwards arrow from bar?\\r%21A7Downwards arrow from bar?\w95ro21ADLeft right wave arrow?\wro@:21AELeft right arrow with stroke?\0+21B0Upwards arrow with tip left?\4+21B1Upwards arrow with tip right?\4%21B2Downwards arrow with tip left?\0%21B3Downwards arrow with tip right?\99[21B6Anticlockwise top semicircle arrow?\55o21B7Clockwise top semicircle arrow?\@r[21BCLeftwards harpoon with barb upwards?\,r[21BDLeftwards harpoon with barb downwards?\,r+21BEUpwards harpoon with barb rightwards?\@r+21BFUpwards harpoon with barb leftwards?\@ro21C0Rightwards harpoon with barb upwards?\,ro21C1Rightwards harpoon with barb downwards?\@r%21C2Downwards harpoon with barb rightwards?\,r%21C3Downwards harpoon with barb leftwards?\o]\[21C4Rightwards arrow over leftwards arrow?\+=\%21C5Upwards arrow left of Downwards arrow?^_721CCRightwards harpoon over leftwards harpoon (equilibrium)?\7[21D0Leftwards double arrow?\7+21D1Upwards double arrow?\7o21D2Rightwards double arrow?\7%21D3Downwards double arrow?\w7ro21D4Left right double arrow?\w7r+21D5Up down double arrow?\1[21E0Leftwards dashed arrow?\1+21E1Upwards dashed arrow?\1o21E2Rightwards dashed arrow?\1%21E3Downwards dashed arrow?\333[27F5Long leftwards arrow?\333o27F6Long rightwards arrow?"_72942Rightwards arrow above short leftwards arrow (equilibrium, trend to the right)?@_72944Short rightwards arrow above leftwards arrow (equilibrium, trend to the left)Note: some arrows may be brailled in more than one way so the above list is not definitive.ShapesThe various shape indicators in UEB are:BrailleDescription$Shape indicator_$Filled shape indicator.$Shaded shape indicator@$Transcriber-defined shape indicator@_$Transcriber-defined solid shape indicator@.$Transcriber-defined shaded shape indicator:Shape terminator&Superposition indicator=Horizontal juxtaposition indicator]Vertical juxtaposition indicator[Physical enclosure indicatorSome specific shapes include:PrintBrailleUnicodeDescription△$#c25B3Triangle□$#d25A1Square○$=25CBCircle?$@#d25B1Parallelogram▲_$#c25B2Filled triangle■_$#d25A0Filled squareSome combined shapes and symbols include:PrintBrailleUnicodeDescription?,.d]"7225CDelta equal to?<def>]"7225DEqual to by definition⊕$=["62295Circled plus?$=["-2296Circled minus?$=["82297Circled times?$=["9229BCircled asterisk operator?$#d["6229ESquared plus?$#d["-229FSquared minus?$#d["822A0Squared times?"/&"822C7Division times?_\=_322A9ForcesTranscriber Defined SignsTranscriber-defined signs may be used where there is no specific UEB encoding for a symbol. Transcriber-defined signs must be described in a note to braille or transcriber note.BrailleDescription@.<Opening transcriber's note indicator@.>Closing transcriber's note indicator?1st transcriber-defined print symbol#?2nd transcriber-defined print symbol@#?3rd transcriber-defined print symbol^#?4th transcriber-defined print symbol_#?5th transcriber-defined print symbol"#?6th transcriber-defined print symbol.#?7th transcriber-defined print symbol@#11st transcriber-defined typeform word indicator@#21st transcriber-defined typeform symbol indicator@#71st transcriber-defined typeform passage indicator@#'1st transcriber-defined typeform terminator^#12nd transcriber-defined typeform word indicator^#22nd transcriber-defined typeform symbol indicator^#72nd transcriber-defined typeform passage indicator^#'2nd transcriber-defined typeform terminator_#13rd transcriber-defined typeform word indicator_#23rd transcriber-defined typeform symbol indicator_#73rd transcriber-defined typeform passage indicator_#'3rd transcriber-defined typeform terminator"#14th transcriber-defined typeform word indicator"#24th transcriber-defined typeform symbol indicator"#74th transcriber-defined typeform passage indicator"#'4th transcriber-defined typeform terminator.#15th transcriber-defined typeform word indicator.#25th transcriber-defined typeform symbol indicator.#75th transcriber-defined typeform passage indicator.#'5th transcriber-defined typeform terminator[March 2019]UK Association for Accessible Formats (UKAAF)Contact details Tel: 0345?608?5223Fax: 0345?608?5224 Email: enquiries@Web: Registered addressUKAAFc/o PiaUnit 42, John Baker Close,Llantarnam Park Industrial Estate, Cwmbr?n NP44 3AWFurther InformationPresident: Lord Low of Dalston CBERegistered charity number: 1126966Registered as a company in England and Wales number: 6748900 ................
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