<!-- Mathematical, Greek and Symbolic characters for HTML -->

<!-- Character entity set. Typical invocation:
     <!ENTITY % HTMLsymbol PUBLIC
       "-//W3C//ENTITIES Symbolic//EN//HTML">
     %HTMLsymbol; -->

<!-- Portions (C) International Organization for Standardization 1986:
     Permission to copy in any form is granted for use with
     conforming SGML systems and applications as defined in
     ISO 8879, provided this notice is included in all copies.
-->

<!-- Relevant ISO entity set is given unless names are newly introduced.
     New names (ie, not in ISO 8879 list) do not clash with any
     existing ISO 8879 entity names. Unicode character numbers
     are given for each character, in hex, and are identical for
     Unicode 1.1 and Unicode 2.0. CDATA values are decimal conversions 
     of the Unicode values. Names are Unicode 2.0 names.
-->

<!-- Latin Extended-B -->
<!ENTITY fnof     CDATA "&#402;"  -- latin small f with hook, =function, =florin, U0192 ISOtech -->

<!-- Greek -->
<!ENTITY Alpha    CDATA "&#913;" -- greek capital letter alpha,  U0391 -->
<!ENTITY Beta     CDATA "&#914;" -- greek capital letter beta,  U0392 -->
<!ENTITY Gamma    CDATA "&#915;" -- greek capital letter gamma,  U0393 ISOgrk3 -->
<!ENTITY Delta    CDATA "&#916;" -- greek capital letter delta,  U0394 ISOgrk3 -->
<!ENTITY Epsilon  CDATA "&#917;" -- greek capital letter epsilon,  U0395 -->
<!ENTITY Zeta     CDATA "&#918;" -- greek capital letter zeta,  U0396 -->
<!ENTITY Eta      CDATA "&#919;" -- greek capital letter eta,  U0397 -->
<!ENTITY Theta    CDATA "&#920;" -- greek capital letter theta,  U0398 ISOgrk3 -->
<!ENTITY Iota     CDATA "&#921;" -- greek capital letter iota,  U0399 -->
<!ENTITY Kappa    CDATA "&#922;" -- greek capital letter kappa,  U039A -->
<!ENTITY Lambda   CDATA "&#923;" -- greek capital letter lambda,  U039B ISOgrk3 -->
<!ENTITY Mu       CDATA "&#924;" -- greek capital letter mu,  U039C -->
<!ENTITY Nu       CDATA "&#925;" -- greek capital letter nu,  U039D -->
<!ENTITY Xi       CDATA "&#926;" -- greek capital letter xi,  U039E ISOgrk3 -->
<!ENTITY Omicron  CDATA "&#927;" -- greek capital letter omicron,  U039F -->
<!ENTITY Pi       CDATA "&#928;" -- greek capital letter pi,  U03A0 ISOgrk3 -->
<!ENTITY Rho      CDATA "&#929;" -- greek capital letter rho,  U03A1 -->
<!-- (there is no Sigmaf, and no U03A2 character either) -->
<!ENTITY Sigma    CDATA "&#931;" -- greek capital letter sigma,  U03A3 ISOgrk3 -->
<!ENTITY Tau      CDATA "&#932;" -- greek capital letter tau,  U03A4 -->
<!ENTITY Upsilon     CDATA "&#933;" -- greek capital letter upsilon,  U03A5 ISOgrk3 -->
<!ENTITY Phi      CDATA "&#934;" -- greek capital letter phi,  U03A6 ISOgrk3 -->
<!ENTITY Chi      CDATA "&#935;" -- greek capital letter chi,  U03A7 -->
<!ENTITY Psi      CDATA "&#936;" -- greek capital letter psi,  U03A8 ISOgrk3 -->
<!ENTITY Omega    CDATA "&#937;" -- greek capital letter omega,  U03A9 ISOgrk3 -->

<!ENTITY alpha    CDATA "&#945;" -- greek small letter alpha, U03B1 ISOgrk3 -->
<!ENTITY beta     CDATA "&#946;" -- greek small letter beta,  U03B2 ISOgrk3 -->
<!ENTITY gamma    CDATA "&#947;" -- greek small letter gamma,  U03B3 ISOgrk3 -->
<!ENTITY delta    CDATA "&#948;" -- greek small letter delta,  U03B4 ISOgrk3 -->
<!ENTITY epsilon     CDATA "&#949;" -- greek small letter epsilon,  U03B5 ISOgrk3 -->
<!ENTITY zeta     CDATA "&#950;" -- greek small letter zeta,  U03B6 ISOgrk3 -->
<!ENTITY eta      CDATA "&#951;" -- greek small letter eta,  U03B7 ISOgrk3 -->
<!ENTITY theta    CDATA "&#952;" -- greek small letter theta,  U03B8 ISOgrk3 -->
<!ENTITY iota     CDATA "&#953;" -- greek small letter iota,  U03B9 ISOgrk3 -->
<!ENTITY kappa    CDATA "&#954;" -- greek small letter kappa,  U03BA ISOgrk3 -->
<!ENTITY lambda   CDATA "&#955;" -- greek small letter lambda,  U03BB ISOgrk3 -->
<!ENTITY mu       CDATA "&#956;" -- greek small letter mu,  U03BC ISOgrk3 -->
<!ENTITY nu       CDATA "&#957;" -- greek small letter nu,  U03BD ISOgrk3 -->
<!ENTITY xi       CDATA "&#958;" -- greek small letter xi,  U03BE ISOgrk3 -->
<!ENTITY omicron  CDATA "&#959;" -- greek small letter omicron,  U03BF NEW -->
<!ENTITY pi       CDATA "&#960;" -- greek small letter pi,  U03C0 ISOgrk3 -->
<!ENTITY rho      CDATA "&#961;" -- greek small letter rho,  U03C1 ISOgrk3 -->
<!ENTITY sigmaf   CDATA "&#962;" -- greek small letter final sigma,  U03C2 ISOgrk3 -->
<!ENTITY sigma    CDATA "&#963;" -- greek small letter sigma,  U03C3 ISOgrk3 -->
<!ENTITY tau      CDATA "&#964;" -- greek small letter tau,  U03C4 ISOgrk3 -->
<!ENTITY upsilon     CDATA "&#965;" -- greek small letter upsilon,  U03C5 ISOgrk3 -->
<!ENTITY phi      CDATA "&#966;" -- greek small letter phi,  U03C6 ISOgrk3 -->
<!ENTITY chi      CDATA "&#967;" -- greek small letter chi,  U03C7 ISOgrk3 -->
<!ENTITY psi      CDATA "&#968;" -- greek small letter psi,  U03C8 ISOgrk3 -->
<!ENTITY omega    CDATA "&#969;" -- greek small letter omega,  U03C9 ISOgrk3 -->
<!ENTITY thetasym    CDATA "&#977;" -- greek small letter theta symbol,  U03D1 NEW -->
<!ENTITY upsih    CDATA "&#978;" -- greek upsilon with hook symbol,  U03D2 NEW -->
<!ENTITY piv      CDATA "&#982;" -- greek pi symbol,  U03D6 ISOgrk3 -->

<!-- General Punctuation -->
<!ENTITY bull     CDATA "&#8226;" -- bullet, =black small circle, U2022 ISOpub  -->
<!-- bullet is NOT the same as bullet operator, U2219 -->
<!ENTITY hellip   CDATA "&#8230;" -- horizontal ellipsis, =three dot leader, U2026 ISOpub  -->
<!ENTITY prime    CDATA "&#8242;" -- prime, =minutes, =feet, U2032 ISOtech -->
<!ENTITY Prime    CDATA "&#8243;" -- double prime, =seconds, =inches, U2033 ISOtech -->
<!ENTITY oline    CDATA "&#8254;" -- overline, =spacing overscore, U203E NEW -->
<!ENTITY frasl    CDATA "&#8260;" -- fraction slash, U2044 NEW -->

<!-- Letterlike Symbols -->
<!ENTITY weierp   CDATA "&#8472;" -- script capital P, =power set, =Weierstrass p, U2118 ISOamso -->
<!ENTITY image    CDATA "&#8465;" -- blackletter capital I, =imaginary part, U2111 ISOamso -->
<!ENTITY real     CDATA "&#8476;" -- blackletter capital R, =real part symbol, U211C ISOamso -->
<!ENTITY trade    CDATA "&#8482;" -- trade mark sign, U2122 ISOnum -->
<!ENTITY alefsym  CDATA "&#8501;" -- alef symbol, =first transfinite cardinal, U2135 NEW -->
<!-- alef symbol is NOT the same as hebrew letter alef, U05D0 although the same glyph
     could be used to depict both characters -->

<!-- Arrows -->
<!ENTITY larr     CDATA "&#8592;" -- leftwards arrow, U2190 ISOnum -->
<!ENTITY uarr     CDATA "&#8593;" -- upwards arrow, U2191 ISOnum-->
<!ENTITY rarr     CDATA "&#8594;" -- rightwards arrow, U2192 ISOnum -->
<!ENTITY darr     CDATA "&#8595;" -- downwards arrow, U2193 ISOnum -->
<!ENTITY harr     CDATA "&#8596;" -- left right arrow, U2194 ISOamsa -->
<!ENTITY crarr    CDATA "&#8629;" -- downwards arrow with corner leftwards, =carriage return, U21B5 NEW -->
<!ENTITY lArr     CDATA "&#8656;" -- leftwards double arrow, U21D0 ISOtech -->
<!-- Unicode does not say that lArr is the same as the 'is implied by' arrow but also 
     does not have any other character for that function. So ? lArr can be used for 
     'is implied by' as ISOtech suggests -->
<!ENTITY uArr     CDATA "&#8657;" -- upwards double arrow, U21D1 ISOamsa -->
<!ENTITY rArr     CDATA "&#8658;" -- rightwards double arrow, U21D2 ISOtech -->
<!-- Unicode does not say this is the 'implies' character but does not have another 
     character with this function so ? rArr can be used for 'implies' as ISOtech suggests -->
<!ENTITY dArr     CDATA "&#8659;" -- downwards double arrow, U21D3 ISOamsa -->
<!ENTITY hArr     CDATA "&#8660;" -- left right double arrow, U21D4 ISOamsa -->

<!-- Mathematical Operators -->
<!ENTITY forall   CDATA "&#8704;" -- for all, U2200 ISOtech -->
<!ENTITY part     CDATA "&#8706;" -- partial differential, U2202 ISOtech  -->
<!ENTITY exist    CDATA "&#8707;" -- there exists, U2203 ISOtech -->
<!ENTITY empty    CDATA "&#8709;" -- empty set, =null set, =diameter, U2205 ISOamso -->
<!ENTITY nabla    CDATA "&#8711;" -- nabla, =backward difference, U2207 ISOtech -->
<!ENTITY isin     CDATA "&#8712;" -- element of, U2208 ISOtech -->
<!ENTITY notin    CDATA "&#8713;" -- not an element of, U2209 ISOtech -->
<!ENTITY ni       CDATA "&#8715;" -- contains as member, U220B ISOtech -->
<!-- should there be a more memorable name than 'ni'? -->
<!ENTITY prod     CDATA "&#8719;" -- n-ary product, =product sign, U220F ISOamsb -->
<!-- prod is NOT the same character as U03A0 'greek capital letter pi' though the same 
     glyph might be used for both -->
<!ENTITY sum      CDATA "&#8721;" -- n-ary sumation, U2211 ISOamsb -->
<!-- sum is NOT the same character as U03A3 'greek capital letter sigma' though the same 
     glyph might be used for both -->
<!ENTITY minus    CDATA "&#8722;" -- minus sign, U2212 ISOtech -->
<!ENTITY lowast   CDATA "&#8727;" -- asterisk operator, U2217 ISOtech -->
<!ENTITY radic    CDATA "&#8730;" -- square root, =radical sign, U221A ISOtech -->
<!ENTITY prop     CDATA "&#8733;" -- proportional to, U221D ISOtech -->
<!ENTITY infin    CDATA "&#8734;" -- infinity, U221E ISOtech -->
<!ENTITY ang      CDATA "&#8736;" -- angle, U2220 ISOamso -->
<!ENTITY and      CDATA "&#8869;" -- logical and, =wedge, U2227 ISOtech -->
<!ENTITY or       CDATA "&#8870;" -- logical or, =vee, U2228 ISOtech -->
<!ENTITY cap      CDATA "&#8745;" -- intersection, =cap, U2229 ISOtech -->
<!ENTITY cup      CDATA "&#8746;" -- union, =cup, U222A ISOtech -->
<!ENTITY int      CDATA "&#8747;" -- integral, U222B ISOtech -->
<!ENTITY there4   CDATA "&#8756;" -- therefore, U2234 ISOtech -->
<!ENTITY sim      CDATA "&#8764;" -- tilde operator, =varies with, =similar to, U223C ISOtech -->
<!-- tilde operator is NOT the same character as the tilde, U007E, although the same 
     glyph might be used to represent both  -->
<!ENTITY cong     CDATA "&#8773;" -- approximately equal to, U2245 ISOtech -->
<!ENTITY asymp    CDATA "&#8776;" -- almost equal to, =asymptotic to, U2248 ISOamsr -->
<!ENTITY ne       CDATA "&#8800;" -- not equal to, U2260 ISOtech -->
<!ENTITY equiv    CDATA "&#8801;" -- identical to, U2261 ISOtech -->
<!ENTITY le       CDATA "&#8804;" -- less-than or equal to, U2264 ISOtech -->
<!ENTITY ge       CDATA "&#8805;" -- greater-than or equal to, U2265 ISOtech -->
<!ENTITY sub      CDATA "&#8834;" -- subset of, U2282 ISOtech -->
<!ENTITY sup      CDATA "&#8835;" -- superset of, U2283 ISOtech -->
<!-- note that nsup, 'not a superset of, U2283' is not covered by the Symbol font 
     encoding and is not included. Should it be, for symmetry? It is in ISOamsn  --> 
<!ENTITY nsub     CDATA "&#8836;" -- not a subset of, U2284 ISOamsn -->
<!ENTITY sube     CDATA "&#8838;" -- subset of or equal to, U2286 ISOtech -->
<!ENTITY supe     CDATA "&#8839;" -- superset of or equal to, U2287 ISOtech -->
<!ENTITY oplus    CDATA "&#8853;" -- circled plus, =direct sum, U2295 ISOamsb -->
<!ENTITY otimes   CDATA "&#8855;" -- circled times, =vector product, U2297 ISOamsb -->
<!ENTITY perp     CDATA "&#8869;" -- up tack, =orthogonal to, =perpendicular, U22A5 ISOtech -->
<!ENTITY sdot     CDATA "&#8901;" -- dot operator, U22C5 ISOamsb -->
<!-- dot operator is NOT the same character as U00B7 middle dot -->

<!-- Miscellaneous Technical -->
<!ENTITY lceil    CDATA "&#8968;" -- left ceiling, =apl upstile, U2308, ISOamsc  -->
<!ENTITY rceil    CDATA "&#8969;" -- right ceiling, U2309, ISOamsc  -->
<!ENTITY lfloor   CDATA "&#8970;" -- left floor, =apl downstile, U230A, ISOamsc  -->
<!ENTITY rfloor   CDATA "&#8971;" -- right floor, U230B, ISOamsc  -->
<!ENTITY lang     CDATA "&#9001;" -- left-pointing angle bracket, =bra, U2329 ISOtech -->
<!-- lang is NOT the same character as U003C 'less than' 
     or U2039 'single left-pointing angle quotation mark' -->
<!ENTITY rang     CDATA "&#9002;" -- right-pointing angle bracket, =ket, U232A ISOtech -->
<!-- rang is NOT the same character as U003E 'greater than' 
     or U203A 'single right-pointing angle quotation mark' -->

<!-- Geometric Shapes -->
<!ENTITY loz      CDATA "&#9674;" -- lozenge, U25CA ISOpub -->

<!-- Miscellaneous Symbols -->
<!ENTITY spades   CDATA "&#9824;" -- black spade suit, U2660 ISOpub -->
<!-- black here seems to mean filled as opposed to hollow -->
<!ENTITY clubs    CDATA "&#9827;" -- black club suit, =shamrock, U2663 ISOpub -->
<!ENTITY hearts   CDATA "&#9829;" -- black heart suit, =valentine, U2665 ISOpub -->
<!ENTITY diams    CDATA "&#9830;" -- black diamond suit, U2666 ISOpub -->