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- .EQ
- delim $$
- tdefine compose % { ~"\h'-0.15m'\
- \v'0.30m'\
- \(de\
- \h'0.15m'\
- \v'-0.30m'" } %
- ndefine compose % ~"o"~ %
- tdefine degree % \(de %
- ndefine degree % { nothing sup o } %
- tdefine circle % \(ci %
- ndefine circle % O %
- tdefine starprod % { ^ down 40 back 13 size +3 roman "*" ^ } %
- ndefine starprod % * %
- tdefine star % { up 8 back 28 size +1 roman "*" } %
- tdefine Star % { up 20 back 16 size +1 roman "*" } %
- ndefine Star % sup roman "*" %
- define quot % ^ \(di ^ %
- tdefine bottom % { "\fB\
- \s7\
- \l'1.10m'\
- \h'-0.55m'\
- \L'-0.80m'\
- \h'0.55m'\
- \v'0.80m'\
- \s0\
- \fP" } %
- ndefine bottom % _| %
- tdefine botbar % { "\fB\
- \s7\
- \l'1.10m'\
- \h'-0.55m'\
- \L'-0.80m'\
- \h'-0.55m'\
- \fP\
- \v'-0.45m'\
- \l'0.7m'\
- \h'0.55m'\
- \v'1.25m'\
- \s0" } %
- ndefine botbar % _| bar %
- tdefine orsign % { ^ "\s-2\
- \h'.05m'\
- \v'.15m'\
- \z\
- \e\
- \e\
- \h'-.08m'\
- \z\(sl\
- \(sl\
- \h'-.1m'\
- \v'-.15m'\
- \s+2" ^ } %
- ndefine orsign % \/ %
- tdefine andsign % { ^ "\s-2\
- \v'.15m'\
- \z\(sl\
- \(sl\
- \h'-.3m'\
- \z\e\
- \e\
- \v'-.15m'\
- \s+2" ^ } %
- ndefine andsign % /\ %
- define xor % { ^ \(ci size +2 { back 70 down 6 + } ~ } %
- define dsum % xor %
- define dprod % { ^ \(ci back 70 times ^ } %
- tdefine exists % { "\s-3\
- \v'.2m'\
- \z\(em\
- \v'-.5m'\
- \z\(em\
- \v'-.5m'\
- \z\(em\
- \v'.85m'\
- \h'.9m'\
- \z\(br\
- \h'.004i'\
- \(br\
- \h'.02m'\
- \v'-.05m'\
- \s+3\
- \h'.2m'" ~} %
- tdefine !exist % { ~ { size -3 "\v'.2m'\
- \z\(em\
- \v'-.5m'\
- \z\(em\
- \v'-.5m'\
- \z\(em\
- \v'.85m'\
- \h'.9m'\
- \z\(br\
- \h'.004i'\
- \(br\
- \h'.02m'\
- \v'-.05m'\
- \h-.1m\
- \h'.3m'" { back 90 down 10 size +3 / }} ^ } %
- tdefine forall % { "\z\e\h'0.5m'\z\(sl\h'-.2m'\v'-.37m'\
- \s-4\fB\l'1m'\fP\s0\v'.37m'\h'0.25m'" ~ } %
- ndefine forall % V- %
- tdefine member % { ^ fat { \(mo } ^ } %
- ndefine member % C- %
- tdefine !member ' { ^ \(mo back 70 / ^ } '
- ndefine !member % C-/ %
- tdefine empty % { size +1 { fat \(es } } %
- ndefine empty % O/ %
- tdefine therefore % { ~ "\s-2\(bu\v'-.5m'\(bu\v'.5m'\(bu\s+2" ~ } %
- ndefine therefore % .. ":" %
- tdefine dotprod % { up 10 size -3 \(bu } %
- ndefine dotprod % oxe %
- tdefine box % { ~ down 25 size 16 \(sq ~ } %
- ndefine box % HIX %
- tdefine endpf % { "\h'.25i'\v'+.35'\s18\
- \(sq\h'-.25m'\v'-.28m'\(sq\v'+.07m'\h'.25m-.25i'\s0" } %
- ndefine endpf % HIXHIX %
- tdefine quad % { "[\h'-12u']" } %
- ndefine quad % [] "_" sup "_" %
- define eq '~=~'
- tdefine !eq % { ~ = back 70 / ~ } %
- ndefine !eq % { ~ = "/" ~ } %
- tdefine equiv % { ~ size -3
- { "\fB\v'-.14'\
- \l'1.2m'\h'-1.2m'\v'-.255m'\
- \l'1.2m'\h'-1.2m'\v'-.25m'\
- \l'1.2m'\fP\v'.645m'" }
- ~ } %
- ndefine equiv '~ == ~'
- tdefine !equiv % { ~
- size -3 { "\fB\
- \v'-.14'\
- \l'1.2m'\h'-1.2m'\v'-.255m'\
- \l'1.2m'\h'-1.2m'\v'-.25m'\
- \l'1.2m'\v'.645m'\fP"}
- back 70 up 2 /
- ~ } %
- ndefine !equiv '~== "/"~'
- tdefine =bydef % { ~ up 45 { \s-1 DELTA } back 65 down 10 { "=" } \s+1 ~ } %
- ndefine =bydef % ="^" %
- tdefine iso % { ~= back 80 up 45 \(ap~ } %
- ndefine iso % ="~" %
- tdefine t- % { ~ "\(~=" ~ } %
- ndefine t- % _"~" %
- tdefine twiddle % \(ap %
- ndefine twiddle % "~" %
- tdefine hat % { up 31 back 75 roman "^" } %
- tdefine Hat % { up 56 back 70 roman "^" } %
- ndefine Hat % hat %
- tdefine tilde % { up 45 back 80 "\(ap" } %
- tdefine Tilde % { up 68 back 74 "\(ap" } %
- ndefine Tilde % tilde %
- define inf % { down 10 fat { size +3 \(if } } %
- tdefine propor % { ~ fat "\s+2\(pt\s-2"~ } %
- ndefine propor % oc %
- tdefine =dot % { ~ = back 49 up 52 size -6 "\(bu" fwd 49 ~ } %
- define ne % { ~ != ~ } %
- define le % { ~ bold <= ~ } %
- define ge % { ~ bold >= ~ } %
- define lt % { ~ < ~ } %
- define gt % { ~ > ~ } %
- tdefine <-> % { ^ <- back 32 -> ^ } %
- ndefine <-> % "<-->" %
- tdefine t< % { ~ "\z<\v'.5m'\(ap\v'-.5m'" ~ } %
- tdefine t> % { ~ "\z>\v'.5m'\(ap\v'-.5m'" ~ } %
- tdefine <=> % { ^ < back 40 = back 30 = back 60 > ^ } %
- ndefine <=> % "<=>" %
- tdefine => % { ^ = back 30 = back 60 > ^ } %
- ndefine => % "==>" %
- tdefine not< % { ~ < back 47 fat "|" ~ } %
- ndefine not< % ~ <| ~ %
- tdefine not> % { ~ > back 57 fat "|" ~ } %
- ndefine not> % ~ |> ~ %
- tdefine div % { ^ fat "|" ^ } %
- ndefine div % ~ | ~ %
- tdefine !div %{ ^ fat "|" {back 40 /} ^ } %
- ndefine !div %^ "|/" ^%
- tdefine ang % { "\s-2\h'+.25m'\
- \v'-0.05m'\(sl\h'-.88m'\v'+0.05m'\l'.6m'\h'+.5m'\s+2" } %
- ndefine ang % /_ %
- tdefine perpto % { ^"\fB\
- \s7\
- \l'0.80m'\
- \h'-0.66m'\
- \L'-0.80m'\
- \h'0.66m'\
- \v'0.80m'\
- \s0\
- \fP" ^ } %
- ndefine perpto % L %
- tdefine l< % { size -3 "\v'-.5m'\
- \(sl\v'+0.7m'\h'-0.87m'\e\v'-.2m'" } %
- ndefine l< % < %
- tdefine r> % { size -3 "\v'-.5m'\
- \e\v'+0.7m'\h'-.6m'\(sl\v'-.2m'\h'-.32m'" } %
- ndefine r> % > %
- define lset % { ^ "{" ~ } %
- define rset % { ~ "}" ^ } %
- tdefine [[ % { [ back 25 [ } %
- ndefine [[ % [[ %
- tdefine ]] % { ] back 25 ] } %
- ndefine ]] % ]] %
- define sthat % ~ | ~ %
- define || % "|" back 10 "|" %
- define lfloor % { \(lf ^ } %
- define rfloor % { ^ \(rf } %
- define lceil % { \(lc ^ } %
- define rceil % { ^ \(rc } %
- define !+- % { ^ up 10 fat { \(+- } ^ } %
- tdefine subset % { ^ \(sb ^ } %
- ndefine subset % C %
- tdefine supset % { ^ \(sp ^ } %
- ndefine supset % "_)" sup "_" %
- tdefine ipsubset % { ^ up 10 \(sb back 72 down 10 "\l'0.35m'\h'0.35m'" ^ } %
- ndefine ipsubset % C_ %
- tdefine ipsupset % { ^ up 10 \(sp back 75 down 10 "\l'0.29m'\h'0.29m'" ^ } %
- ndefine ipsupset % "_" sup "_" "/)" %
- tdefine ipincl % { ~ "\v'-.35m'\s-1\z\h'+.1m'\
- \s-3\(or\s+3\h'-.2m'\v'-.35m'\z\
- \(em\v'.7m'\z\(em\v'.3m'\(em\v'-.55m'\s+1\h'+.1m'\v'+.3m'" ~ } %
- ndefine ipincl % C_ %
- tdefine incl % { ~ back 25 up 10 { size -4 up 10 { fat "|" } size -1
- { back 24 down 28 fat "\(em" back 86 up 46 fat "\(em" } } ~ } %
- ndefine incl % ~ [ ~ %
- tdefine lub % { ~ size -1
- { fat "|" back 31 down 41 fat "\(em" back 13 fat "|" } ~ } %
- tdefine glb % { ~ size -1
- { fat "|" back 30 up 61 fat "\(em" back 13 fat "|" } ~ } %
- tdefine reals % { roman { I back 20 R } } %
- ndefine reals % "RR" %
- tdefine natnums % { roman { I back 20 N } } %
- ndefine natnums % "NN" %
- define complex % { ~ { roman C back 50 up 20 { fat size -10 "|" }} ~ } %
- define rationals % { ~ { roman Q back 50 up 20 { fat size -10 "|" }} ~ } %
- define ints % { ~ { roman Z back 100 roman Z } ~ } %
- define xlist % { x sub 1 ,..., x sub n } %
- define xsubi % { x sub i } %
- define xsubj % { x sub j } %
- tdefine quarter % { size -3 {up 70 fwd 2 roman "1" }}
- back 54 { size +3 roman "/" } size -2 {back 60 up 10 roman "4" } %
- ndefine quarter % 1/4 %
- tdefine 3quarter % { size -3 {up 67 back 10 roman "3" }}
- back 54 { size +3 roman "/" } size -2 {back 60 up 5 roman "4" } %
- ndefine 3quarter % 3/4 %
- define where % { ~ bold "where" ~ } %
- define iff % { ~ roman "if and only if" ~ } %
- tdefine nbyn % { n back 10 times n } %
- ndefine nbyn % { n times n } %
- tdefine mbyn % { m back 15 times n } %
- ndefine mbyn % { m times n } %
- .EN
-