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#
# Mathematical operators
# Range: 2200–22FF
#
# Miscellaneous mathematical symbols
<Multi_key> <Multi_key> <A> <A> : "∀" U2200 # FOR ALL
# = universal quantifier
<Multi_key> <Multi_key> <p> <a> <r> <t> : "∂" U2202 # PARTIAL DIFFERENTIAL
<Multi_key> <Multi_key> <p> <d> <i> <f> : "∂" U2202 # PARTIAL DIFFERENTIAL
<Multi_key> <Multi_key> <E> <E> : "∃" U2203 # THERE EXISTS
# = existential quantifier
<Multi_key> <Multi_key> <slash> <E> <E> : "∄" U2204 # THERE DOES NOT EXIST
<Multi_key> <Multi_key> <l> <a> <p> : "∆" U2206 # INCREMENT
# = Laplace operator
# = forward difference
# = symmetric difference (in set theory)
<Multi_key> <Multi_key> <d> <i> <f> : "∆" U2206 # INCREMENT
<Multi_key> <Multi_key> <d> <i> <f> <f> : "∆" U2206 # INCREMENT
<Multi_key> <Multi_key> <d> <e> <l> : "∇" U2207 # NABLA
# = backward difference
# = gradient, del
# Set membership
<Multi_key> <Multi_key> <i> <n> : "∈" U2208 # ELEMENT OF
<Multi_key> <Multi_key> <exclam> <i> <n> : "∉" U2209 # NOT AN ELEMENT OF
<Multi_key> <Multi_key> <slash> <i> <n> : "∉" U2209 # NOT AN ELEMENT OF
<Multi_key> <Multi_key> <n> <i> : "∋" U220B # CONTAINS AS MEMBER
# = such that
<Multi_key> <Multi_key> <exclaim> <n> <i> : "∌" U220C # DOES NOT CONTAIN AS MEMBER
<Multi_key> <Multi_key> <slash> <n> <i> : "∌" U220C # DOES NOT CONTAIN AS MEMBER
# Miscellaneous mathematical symbol
<Multi_key> <Multi_key> <Q> <E> <D> : "∎" U220E # END OF PROOF
# = q.e.d.
<Multi_key> <Multi_key> <q> <e> <d> : "∎" U220E # END OF PROOF
# N-ary operators
<Multi_key> <Multi_key> <p> <r> <o> <d> : "∏" U220F # N-ARY PRODUCT
# = product sign
<Multi_key> <Multi_key> <s> <u> <m> : "∑" U2211 # N-ARY SUMMATION
# = summation sign
# Operators
<Multi_key> <Multi_key> <minus> <period> : "−" U2212 # MINUS
<Multi_key> <Multi_key> <minus> <plus> : "∓" U2213 # MINUS-OR-PLUS SIGN
<Multi_key> <Multi_key> <slash> <slash> : "∕" U2215 # DIVISION SLASH
<Multi_key> <Multi_key> <d> <i> <v> : "∕" U2215 # DIVISION SLASH
# • generic division operator
<Multi_key> <Multi_key> <asterisk> <o> : "∘" U2218 # RING OPERATOR
# = composite function
# = APL jot
# SQUARE ROOT exists as:
# <Multi_key> <v> <slash>
# <Multi_key> <slash> <v>
<Multi_key> <Multi_key> <3> <v> <slash> : "∛" U221B # CUBE ROOT
<Multi_key> <Multi_key> <4> <v> <slash> : "∜" U221C # FOURTH ROOT
<Multi_key> <Multi_key> <8> <3> : "∝" U221D # PROPORTIONAL TO
# Angles
<Multi_key> <Multi_key> <bar> <underscore> : "∟" U221F # RIGHT ANGLE
<Multi_key> <Multi_key> <slash> <underscore> : "∠" U2220 # ANGLE
<Multi_key> <Multi_key> <parenright> <slash> <underscore> : "∡" U2221 # MEASURED ANGLE
# Logical and set operators
<Multi_key> <Multi_key> <slash> <backslash> : "∧" U2227 # LOGICAL AND
# = wedge, conjunction
<Multi_key> <Multi_key> <backslash> <slash> : "∨" U2228 # LOGICAL OR
# = vee, disjunction
<Multi_key> <Multi_key> <braceleft> <asciicircum> : "∩" U2229 # INTERSECTION
# = cap, hat
<Multi_key> <Multi_key> <braceleft> <U> : "∪" U222A # UNION
# = cup
# Integrals
<Multi_key> <Multi_key> <i> <n> <t> : "∫" U222B # INTEGRAL
<Multi_key> <Multi_key> <i> <i> <n> <t> : "∬" U222C # DOUBLE INTEGRAL
<Multi_key> <Multi_key> <i> <i> <i> <n> <t> : "∭" U222D # TRIPLE INTEGRAL
<Multi_key> <Multi_key> <o> <i> <n> <t> : "∮" U222E # CONTOUR INTEGRAL
<Multi_key> <Multi_key> <o> <i> <i> <n> <t> : "∯" U222F # SURFACE INTEGRAL
<Multi_key> <Multi_key> <o> <i> <i> <i> <n> <t> : "∰" U2230 # VOLUME INTEGRAL
# Relations
<Multi_key> <Multi_key> <tilde> <period> : "∼" U223C # TILDE OPERATOR
# = varies with (proportional to)
# = difference between
# = similar to
# = not
# = cycle
# = APL tilde
# Miscellaneous mathematical symbol
<Multi_key> <Multi_key> <s> <i> <n> <e> : "∿" U223F # SINE WAVE
# = alternating current
# Relations
<Multi_key> <Multi_key> <slash> <tilde> <period> : "≁" U2241 # NOT TILDE
<Multi_key> <Multi_key> <tilde> <slash> : "≁" U2241 # NOT TILDE
<Multi_key> <Multi_key> <tilde> <minus> : "≃" U2243 # ASYMPTOTICALLY EQUAL TO
<Multi_key> <Multi_key> <minus> <tilde> : "≃" U2243 # ASYMPTOTICALLY EQUAL TO
<Multi_key> <Multi_key> <slash> <tilde> <minus> : "≄" U2244 # NOT ASYMPTOTICALLY EQUAL TO
<Multi_key> <Multi_key> <tilde> <minus> <slash> : "≄" U2244 # NOT ASYMPTOTICALLY EQUAL TO
<Multi_key> <Multi_key> <tilde> <equal> : "≅" U2245 # APPROXIMATELY EQUAL TO
<Multi_key> <Multi_key> <equal> <tilde> : "≅" U2245 # APPROXIMATELY EQUAL TO
<Multi_key> <Multi_key> <tilde> <slash> <equal> : "≆" U2246 # APPROXIMATELY BUT NOT ACTUALLY EQUAL TO
<Multi_key> <Multi_key> <equal> <slash> <tilde> : "≆" U2246 # APPROXIMATELY BUT NOT ACTUALLY EQUAL TO
<Multi_key> <Multi_key> <tilde> <equal> <slash> : "≇" U2247 # NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
<Multi_key> <Multi_key> <slash> <tilde> <equal> : "≇" U2247 # NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
<Multi_key> <Multi_key> <tilde> <tilde> : "≈" U2248 # ALMOST EQUAL TO
# = asymptotic to
<Multi_key> <Multi_key> <slash> <tilde> <tilde> : "≉" U2249 # NOT ALMOST EQUAL TO
<Multi_key> <Multi_key> <tilde> <tilde> <slash> : "≉" U2249 # NOT ALMOST EQUAL TO
<Multi_key> <Multi_key> <tilde> <tilde> <minus> : "≊" U224A # ALMOST EQUAL OR EQUAL TO
<Multi_key> <Multi_key> <equal> <d> <e> <f> : "≝" U225D # EQUAL TO BY DEFINITION
<Multi_key> <Multi_key> <d> <e> <f> <equal> : "≝" U225D # EQUAL TO BY DEFINITION
<Multi_key> <Multi_key> <equal> <question> : "≟" U225F # QUESTIONED EQUAL TO
<Multi_key> <Multi_key> <equal> <minus> : "≡" U2261 # IDENTICAL TO
<Multi_key> <Multi_key> <minus> <equal> : "≡" U2261 # IDENTICAL TO
<Multi_key> <Multi_key> <slash> <equal> <minus> : "≢" U2262 # NOT IDENTICAL TO
<Multi_key> <Multi_key> <slash> <minus> <equal> : "≢" U2262 # NOT IDENTICAL TO
<Multi_key> <Multi_key> <equal> <minus> <slash> : "≢" U2262 # NOT IDENTICAL TO
<Multi_key> <Multi_key> <minus> <equal> <slash> : "≢" U2262 # NOT IDENTICAL TO
# LESS-THAN OR EQUAL TO and GREATER-THAN OR EQUAL TO exist as:
# <Multi_key> <less> <underscore> : "≤" U2264 # < _ LESS-THAN OR EQUAL TO
# <Multi_key> <underscore> <less> : "≤" U2264 # _ < LESS-THAN OR EQUAL TO
# <Multi_key> <greater> <underscore> : "≥" U2265 # > _ GREATER-THAN OR EQUAL TO
# <Multi_key> <underscore> <greater> : "≥" U2265 # _ > GREATER-THAN OR EQUAL TO
<Multi_key> <Multi_key> <less> <equal> : "≦" U2266 # LESS-THAN OVER EQUAL TO
<Multi_key> <Multi_key> <equal> <less> : "≦" U2266 # LESS-THAN OVER EQUAL TO
<Multi_key> <Multi_key> <greater> <equal> : "≧" U2267 # GREATER-THAN OVER EQUAL TO
<Multi_key> <Multi_key> <equal> <greater> : "≧" U2267 # GREATER-THAN OVER EQUAL TO
<Multi_key> <Multi_key> <less> <slash> <equal> : "≨" U2268 # LESS-THAN BUT NOT EQUAL TO
<Multi_key> <Multi_key> <equal> <slash> <less> : "≨" U2268 # LESS-THAN BUT NOT EQUAL TO
<Multi_key> <Multi_key> <greater> <slash> <equal> : "≩" U2269 # GREATER-THAN BUT NOT EQUAL TO
<Multi_key> <Multi_key> <equal> <slash> <greater> : "≩" U2269 # GREATER-THAN BUT NOT EQUAL TO
<Multi_key> <Multi_key> <plus> <less> : "≪" U226A # MUCH LESS-THAN
<Multi_key> <Multi_key> <plus> <greater> : "≫" U226B # MUCH GREATER-THAN
<Multi_key> <Multi_key> <slash> <less> : "≮" U226E # NOT LESS-THAN
<Multi_key> <Multi_key> <less> <slash> <period> : "≮" U226E # NOT LESS-THAN
<Multi_key> <Multi_key> <slash> <greater> : "≮" U226E # NOT GREATER-THAN
<Multi_key> <Multi_key> <greater> <slash> <period> : "≮" U226E # NOT GREATER-THAN
<Multi_key> <Multi_key> <slash> <less> <underscore> : "≰" U2270 # NEITHER LESS-THAN NOR EQUAL TO
<Multi_key> <Multi_key> <underscore> <less> <slash> : "≰" U2270 # NEITHER LESS-THAN NOR EQUAL TO
<Multi_key> <Multi_key> <slash> <greater> <underscore> : "≱" U2271 # NEITHER GREATER-THAN NOR EQUAL TO
<Multi_key> <Multi_key> <underscore> <greater> <slash> : "≱" U2271 # NEITHER GREATER-THAN NOR EQUAL TO
<Multi_key> <Multi_key> <tilde> <less> : "≲" U2272 # LESS-THAN OR EQUIVALENT TO
<Multi_key> <Multi_key> <less> <tilde> : "≲" U2272 # LESS-THAN OR EQUIVALENT TO
<Multi_key> <Multi_key> <tilde> <greater> : "≳" U2273 # GREATER-THAN OR EQUIVALENT TO
<Multi_key> <Multi_key> <greater> <tilde> : "≳" U2273 # GREATER-THAN OR EQUIVALENT TO
<Multi_key> <Multi_key> <braceleft> <parenleft> : "⊂" U2282 # SUBSET OF
# = included in set
<Multi_key> <Multi_key> <braceleft> <parenright> : "⊃" U2283 # SUPERSET OF
# = includes in set
<Multi_key> <Multi_key> <slash> <braceleft> <parenleft> : "⊄" U2284 # NOT A SUBSET OF
<Multi_key> <Multi_key> <slash> <braceleft> <parenright> : "⊅" U2285 # NOT A SUPERSET OF
<Multi_key> <Multi_key> <braceleft> <underscore> <parenleft> : "⊆" U2286 # SUBSET OF OR EQUAL TO
<Multi_key> <Multi_key> <braceleft> <underscore> <parenright> : "⊇" U2287 # SUPERSET OF OR EQUAL TO
<Multi_key> <Multi_key> <slash> <braceleft> <underscore> <parenleft> : "⊈" U2288 # NEITHER A SUBSET OF NOR EQUAL TO
<Multi_key> <Multi_key> <slash> <braceleft> <underscore> <parenright> : "⊉" U2289 # NEITHER A SUPERSET OF NOR EQUAL TO
<Multi_key> <Multi_key> <braceleft> <underscore> <slash> <parenleft> : "⊊" U228A # SUBSET OF WITH NOT EQUAL TO
<Multi_key> <Multi_key> <braceleft> <underscore> <slash> <parenright> : "⊋" U228B # SUPERSET OF WITH NOT EQUAL TO
# Operators
<Multi_key> <Multi_key> <bar> <minus> : "⊢" U22A2 # RIGHT TACK
# = turnstile
# = proves, implies, yields
# = reducible
<Multi_key> <Multi_key> <minus> <bar> : "⊣" U22A2 # LEFT TACK
# = reverse turnstile
# = non-theorem, does not yield
# Miscellaneous mathematical symbols
<Multi_key> <Multi_key> <minus> <bar> <minus> : "⊤" U22A4 # DOWN TACK
# = top
<Multi_key> <Multi_key> <underscore> <bar> <underscore> : "⊥" U22A5 # UP TACK
# = base, bottom
# Operators
<Multi_key> <Multi_key> <v> <underscore> : "⊻" U22BB # XOR
<Multi_key> <Multi_key> <underscore> <v> : "⊻" U22BB # XOR
<Multi_key> <Multi_key> <backslash> <underscore> <slash> : "⊻" U22BB # XOR
<Multi_key> <Multi_key> <asciicircum> <minus> : "⊼" U22BC # NAND
<Multi_key> <Multi_key> <minus> <asciicircum> : "⊼" U22BC # NAND
<Multi_key> <Multi_key> <slash> <minus> <backslash> : "⊼" U22BC # NAND
# Operators
<Multi_key> <Multi_key> <asterisk> <period> : "⋅" U22C5 # DOT OPERATOR
# • preferred to 00B7 · for denotation of
# multiplication
# Relations
<Multi_key> <Multi_key> <bar> <period> <period> : "⋮" U22EE # VERTICAL ELLIPSIS
# • these four ellipses are used for matrix
# row/column elision
<Multi_key> <Multi_key> <minus> <period> <period> : "⋯" U22EF # MIDLINE HORIZONTAL ELLIPSIS
<Multi_key> <Multi_key> <slash> <period> <period> : "⋰" U22F0 # UP RIGHT DIAGONAL ELLIPSIS
<Multi_key> <Multi_key> <backslash> <period> <period> : "⋱" U22F1 # DOWN RIGHT DIAGONAL ELLIPSIS
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