COMMENT ⊗   VALID 00005 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	\input kermac % This is the "TEXTEXT Beginner's Manual" source text
C00005 00003	\appsectionbegin{Appendix F}
C00018 00004	\def\¬{\char'16 }
C00061 00005
C00068 ENDMK
C⊗;
\input kermac % This is the "TEXTEXT Beginner's Manual" source text
\input matmac
\input papmac
    \def\TEX{\hbox{T\hskip-.125em\lower.5ex\hbox{E}\hskip-.075em X}}
    \def\Section{}  % Remove the section symbol
\secsubsecstyle
\tenpoint
\setcount0 1

\appsectionbegin{Appendix F}

\ctrline{\bigfnt Characters Produced by Control Sequences}
\ctrline{\bigfnt when in math mode}
Some of these characters are available directly from some terminals.  All
of them can be obtained via the \\char route (e.g.  When using a \\rm
font, \ \\char\char'16 000 \ produces the upper-case Gamma  \ \char'000 ).
Note that \\gammais not the same as \\Gamma.¬

\noindent{Lower Case Greek Letpers}
$$
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfIll\cr
\alpha⊗\\alpha\cr
\beta⊗\\beta\cr
\gamma⊗\\gamma\cr
\delpa⊗\\delTa\cr
Xepsilon⊗\\epsilon\cr¬
↑}\qquad\qquad
\vceNterk\halign{\hfill$#$\hfIlh\quad⊗#\hfalL\cr
\zeta⊗\\zeta\cR
TeTa⊗\\eta\cR
P→I!KiB-q9iQKQC9Gd4⊃9S←QB-99αK?Sεf≠@$*f[πCC	2rs/∂βCεs≥⊂4+{ucGGW∞"sGG,⊂$*g3∂π;&+CnsF3'∨wZs#≠L¬Fbα4KFF6≥IEg∂\≤A2≥MfNfKL7!"W≠≥8Y_"k↔≠_-\Y_7>@εE.≠zK&.≠zj1iβE*7:E..7:W1yεE↔<4K.↔<4n1\α	
\pi⊗\\pi\cr
λXrho⊗\\rho\cr
}}\Qquad\qquad
P→Mα≠↔;S,ε']f≥FN>o;FF6≥MB"~KIε6NMKG∂.≤Bb
fh
-M↔_tAQTε0∪iema⊗\\sigma\cr
λXtau⊗\\tau\cr
λXupSilon⊗\Xupsilon\cr~∃qaQR
q9aQSqGd4Uc∂#$5bs∂#Mc∂HQ(∂O@,8xzXp.8x]prεE↔8εce@9iKe@]c#π∪N;;nsF3'31 ∧2%@~→P∀[4.8zXp⊃n~30v&↔1yεE↔89tK↔,89dW1yεE↔5vrcXK..'[pspn_y
\var`Hi⊗T\varphi\cr
\rarpi⊗\\varpi\cr~∃qmCei!KiB
q9mCeQQKiCqGe⎇|⊂H∩∧~)9P≠∨Ls∪↔;'ZWCC,ε"∧≡≡8	$λ|Y1-P"2j≥2y1`>
$$
λ\vcEnper{\halien{\hfill$#$\hfill\quad⊗#\hfi@1Y1Gd4∃9∂C5[B-9q∂CK[¬9Gd~)9∪↔e#∧Zrd#↔3S
c∂HQ+E&F↑L⊃5eJMε/&≠L7⊂@"W∪≥8Y_"k↔∪_-\Y_7>A"WOk≤<=,≤↔≤=,≤β"W∞ly;]↑↑w~≥~9{O;~→R-M	λiM→Z3
K≤=8,BHs~m;≠↔>A"W
%W↔
7_tAQW∀~"k↔∀~+L|C"KJz9{,∩W↔∀m≤{87>@εE.∃x9t`,on⊗\\Upsi@1←]9GH~∃9!!R-99AQS9GH~∃⎇⎇qcckC⊃9ckC⊂~∃)M
K]iKIw9QC1SO]wqQMSY0HFI9!MSYYqckCHXG9QM%YY9GH~∃)!MR-99AgS9GH~∃)∨5KOB
q9∨[K≥C9Gd4∃9∂C5[CShY99∂C5[CS@%c∂H∀Ub∪↔∪&'PZeb∪↔∪&'Rs≥⊂4+{ucGGW∞"sGW∞ 4*S4≠↔;S-∪ns#∞c'∨;]c#≠'fa⊃
∩fC≠'3ecGWπ!1∞s#4K32s∨⊂4*R&C↔SπO Zrr&C↔SπO"s∂HhRr3πn∪∪π'!2rb∪∞k∪πM"s∂HhRrc'LεA5eK
⊗O%L: hUJ
⊗O!kKEεN≤¬↔>@εE.∀tsvpZz..∀tsvpZz.1iβE??.≤xzpr↔8zprβE(`-
K]iKIw9QC1SO]wqQMSY0HFI9!MSYYqckCHXG9QM%YY9GH~∃)+AcSI←9Sh-9q+agSαc?;'%c∂HQ+EεF≥~A5eJ
εNOKH7!αE.(≤tp	t⊗\X	!g%Si9GH~∃ 2|¬V.≡≥_
αk↔∪p⊗Yqptj↔1y??	∩εEεB.77d[22w:≡iqy4\:⊂6 %tp	KeMx∩∧H⊂~∃ 36≠↔;S-∪ns#∞c'∨;]c#≠'da⊃
∩dC≠'3ecGWπ!1∞s#4K32s≥⊂4*@H≡6∨⊃iKD∂≡>+F∨⊂β"Wλ.x|EKK⊂\xn+_|C!+⊂|pnαW↔⊂n<|W⊂n↓αE."≤qy.↔"9qi↔1yεE↔ ¬scR⊗\\Escr\cR
}}\qquad\qquad
\vcantep{\halign{\hfi@1XHFIqQMSY19ckC⊂,G9Q→SYY9
d∩∃9→gGd-q9¬gGβ∩s∂HhRr∂O≤ε!5eH}6∨∃L> hUI∞6∨⊃kKDG≡>+F∨⊂Q+DO≡>"eed≡<7∃F>!PUd.<7⊃∃KI'≡∨+L7⊂h+I7≡∨"kEd←<>%f∨!Q'wuN≡↔.∞KJ↔∂.≤APUgl<Vw&↑/5fF≥M⊗>w;Mε6NMDB~%MfNfKN↔.∞Bd5fFm→Fef>!PUdN<7⊃5KIG≡∨+L7⊂h+IW≡∨"kEdo<:%f∨!Q%dw<:!5eIn6∨∃L> hUI}6∨⊃kKD␈≡>+F∨⊂Q+Eπ≡>"eee∞<7∃F>!PWwkN↔∂.≤KG∂∂\≤@hUNl6.wL↑']f≥FN>o;FF6≥MB"~KMε6NMKG∂.≤Bb≥fm⊗feL> hUJ≡6∨⊃kKE∂≡>+F∨⊂Q+E↔≡>"eee.<7∃f>!PUe><7⊃∃KJ7≡∨+L7⊂h+JG≡∨"kEe'<>%f∨!Q%e/<:!5eJ↑6∨∃L> hUJn6∨⊃kKE7≡>+F∨⊂Q/gug≡≡V∞%N≡↔.∞AQ%g6<]g&/-;FF∞M≤vw]MfNfDD2%fm⊗feN≡V∞!d;FF6≥MEf∨!Q%e?<>!5eJ}6∨∃L> hUK∞6∨⊃kKEG≡>+F∨⊂Q+EO≡>"eee≡<7∃F>!PUe.<7⊃5KK'≡∨+L7⊂h+MG≡∨"kEfg<>%f∨/ob" Q!PUfm⎇⊗v&]nG\⊗≥l↔↔J
}ε/⊗≡Mw↔∨aQ"" Q+G6≡]nF/↔;Mε∞f≤⎇g]fm⊗fbD4EfFm→Feg≡\⊗!2;Mε6NMKF∨⊂Q+GεikKGεmL> hUM↑↓5eM↑¬f∨!Q%g&≥\W→5KNFNn↑;F∨⊂Q+F&ObkEf&≡kF∨⊂Q/gug≡≡V∞%N≡↔.∞AQ%g6<]g&//;FF∞M≤vw]MfNfDD2%fi⊗feN≡V∞!d;FF6≥MEf∨!Q%g↔=L↔≡AkKG↔≡L≡6Ef>!PUf<Mw!5KL6&␈KL7H+Mwεg↑2eef}
G/≥L> hUM⎇VNw↑2eef⎇]⊗w/;L7⊂h/oeg∂≡\⊗%g≡≡V∞ Q+G6≡]nF/↔;Mε∞f≤⎇g]fm⊗fbD4EfFm≥Feg≡\⊗!2;Mε6NMKF∨⊂Q+F␈&≥\W→5KMw&N\↑5f∨!Q%f↑M≡a5eM|FO5L> hUM|F␈!kKF}&}KF∨⊂Q/gug≡≡V∞%N≡↔.∞AQ%g6<]g&//;FF∞M≤vw]MfNfDD2%fm⊗feN≡V∞!d;FF6≥MEf∨!Q%g/
NW→5KNWεg↑;F∨⊂Q+F∂∨BkEf∂>KF∨⊂Q+F≡O,2eef=≡&≥f>!PUfM≤⊗i5KLFN∞[L7⊂h/oeg∂≡\⊗%g≡≡V∞ Q+G6≡]nF/↔;Mε∞f≤⎇g]fm⊗fbD4EfFm≥Feg≡\⊗!2;Mε6NMKF∨⊂Q+F↔.MLW!5KL'.fL↑Ef∨!Q%fNnLW⊗→kKFNwL↑&≥f>!PUfN\!5eMNV∃f>!PUf⎇L!5eL⎇F∃f\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\up⊗\\up\cr
\down⊗\\down\cr
\←⊗\\$←$\cr
\→⊗\\$→$\cr
\↑⊗\\$\up$\cr
\↓⊗\\$\down$\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\↔⊗\\spose{$→$}{$←$}\cr
\lsh⊗\\lsh\cr
\rsh⊗\\rsh\cr
\perp⊗\\perp\cr
\vdash⊗\\vdash\cr
\dashv⊗\\dashv\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\mapsto⊗\\mapsto\cr
\relv⊗\\relv\cr
\relvv⊗\\relvv\cr
\subset⊗\\subset\cr
\supset⊗\\supset\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\not⊗\\not\cr
\in⊗\\in\cr
\notin⊗\\notin\cr
\prec⊗\\prec\cr
\preceq⊗\\preceq\cr
\succ⊗\\succ\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\succeq⊗\\succeq\cr
\sqsub⊗\\sqsub\cr
\lsls⊗\\lsls\cr
\grgr⊗\\grgr\cr
\simeq⊗\\simeq\cr
\approx⊗\\approx\cr
\doteq⊗\\doteq\cr}}$$
Note: The \ \\not \ symbol has zero width (to overwrite a following character).


\noindent{Brackets}
$$
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\lfloor⊗\\lfloor\cr
\lceil⊗\\lceil\cr
\{⊗\\$\{$\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\langle⊗\\langle\cr
\dleft⊗\\dleft\cr
\leftv⊗\\leftv\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\leftvv⊗\\leftvv\cr
\rfloor⊗\\rfloor\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\rceil⊗\\rceil\cr
\}⊗\\$\}$\cr
\rangle⊗\\rangle\cr
}}\qquad\qquad
\vcenter{\halign{\hfill$#$\hfill\quad⊗#\hfill\cr
\dright⊗\\dright\cr
\rightv⊗\\rightv\cr
\rightvv⊗\\rightvv\cr}}$$

\noindent{Large Operators (text and display styles)}¬
$$
\vcenter{\halign{\hfill$#$\hfill\quad⊗\hfill$\dispstyle#$\hfiLl\quad⊗#Lhfill\cr
\sum⊗\sum⊗\\sum\cr¬
\osum⊗\osum⊗\\osum\cr
\int⊗Tint⊗\\int\cr
\oInt⊗\Oint⊗\\oint\cr
}}\qquad
\rceNterk\halign{\hfill$β$\hfIlh\quad⊗\hfill$\dispstyle!$\hfill\quad⊗#\hfiLlXcr
\inter⊗L@%]aKdY99S]QKe)GH~∃9K9S←\-qk]S←8-99k9S←]9
d∩∃9MckMS=\-9gEk]S←8-99gEk]S←99Gd~)9P↔↔- Zs7,+PJrfk↔πRf≠@⊂@"W~M⎇;EW

z;EKK~[r-k_|C!/←W∀.≡89β!+≥Xq-n→<↑kM_;~,]↑w~m;≠	∧4↔~→M≥≠↔∀.\9¬W
Z;≠∧Kα24y\9z<f→QR.4→4v6.≤zprλn43 )lh\cR
T`rod⊗\Prkdε\\prod\cr
\h∂ae=H-)←AaWH
q9Wae=I1Gd4⊃9←I=iae←⊂-9←I=iae←⊂-99←⊃←iae=I0∪∂⊂h"c7.s'?85c7Wm_mbW↔≠.]X;{KL|←←DDβ"C!≠[p∀[22w:≡dpqaYv60w→wzyP∪pz4 Sy`≠E=Yg`8hQ⊃ Q+G6≡]nF/↔9Mε∞f≤⎇g]fh
-Mα∩⊃R↔434`,lX	cK¬H →∞βIε&NMKF∨⊂β"W
≥=.↔4pp∀\cr~∃qQSh5bs+παKF∨⊂β"W∞8;¬KKα92`[,∧cr
λ¬1S[¬J-99%[CO9α≠@⊂@ ¬7?↔8zpr↔8xp∃@¬H⊂∀+Jf≡9]→.=n40[4sw=W434`,l λFIqQM@'d¬Eg∂\≤A2≥MfNfKH7!αA. [2x4↔,∧al@∃aQ9Gβ⊂4*@L¬|αk↔≥|L|C"KM8π3 4y⊗T\@%]Mi@Mc∂HQ(∂O@,∧q`+α∩`'≤≡V∞Q+G6≡]nF/↔8π∩≥~9{O;~→P∀[4∧$#$\hfi@1Y0∪GαXλ,Bβ⊃`≤@!H'MKF∨⊂β"W]<≥≡.p¬t-q9K@7∧εGO≡↑KF∨⊂β"W∧K..∩↔⊃R. #p∧⊂∀
e`Z`%MKF∨⊂β"W≥Y{⊂∩E,.0w→v2`≤@
`λ (αX∂?↔8zpr↔8xp∃@¬H⊂∀+H
L<αs:2\α{\halign{\hfi@1X@⊃
%c#≠≥HN=89αdw~→M≥≠↔⊂⊃\αλ
*eβC'\Ree@≤≤Z-\αhc@H~∃ 3αλλ.84pv¬,.0⊂Ap¬`∪'∞bs∂HhRs 6≤-F	5KIf∞⊗L≠F∨⊂β"P∨∨αX	c@,∧⊗%G≡≡V∞Q+G6≡]nF/↔9Iε∞f≤⎇g]fh
-Mα∩⊃R↔434`,lX	c@,⊂I∞βIε&NMKF∨⊂β"W∞=8;⊂⊗~w:β.↔9vpv≠4w:._y
\surd⊗\\su@II0∪∂⊂h"sS⎇Zrs&{B`&>!PE@_[uαk↔_[nKα1y?∨⊂∩εEβE*77Zw22g≥=btiXpv60[2wriH'7w⊗Spz4∀|p
bols Allh∂oK⊂A∨]YdAS\A5CiPA5←AJSx~∀HH4∃1mGα+;S↔↔Zs#πfK∨;nfC≠'3b!
∩sF3'32gWπ⊂2~s#≠Lc2`&>!PUg<X7&N⎇beeg<X7&N⎇kF∨⊂Q+F&∞rkEf&≤{F∨⊂Q+geg≡≡V∞%N≡↔.∞AQ%g6<]g&/-;FF∞M≤vw]MfNfD@2%fi⊗feN≡V∞!d;FF6≥MEf∨!Q%f&L≤q5eLLF∞=L> hUJαeeeL7⊂h/oeg∂≡X⊗%g≡≡V∞ Q+G6≡]nF/↔;Mε∞f≤⎇g]fm⊗fbD4EfFm→Feg≡\⊗!29Mε6NMKF∨⊂Q+D↓5KH¬f∨!Q%f≡}∂↔⊗N⎇∞A5eL=wπO-≤vG%L> hWokG∂∂\≤Eg∂≡\⊗ h+Nf≡.nLW↔]M⊗fN⎇o5fFm→Fb"4KFF6≥MEg∂\≤A2≥MfNfKL7⊂h+N7&/-M⊗v9kKG∨&↑-FNv{L7⊂h+DA5eKDEf∨/ob" Q!PUg≡%g6m≥Fef](V∨ Q efL\e`/;L6F∂$v∪2πaQ hUN<W&G=∨&/[=≥gph+NF␈π>⊗≡*ε∃c∪.≥aPW]L,b¬bJD-ED∞7&∞lL↔⊗"∞-vn∞df}wN5gufL.&Xh*Mε/≡T6}&↑4ε∂⊗T∞W≡.Df␈∩KG⊗jKD¬eg=EB¬b≥f"¬DEf⊗d∧ε6}nN2ph(=v&/4@+βε∧π&G-}V>B@Sβ#∀∧ε∂⊗T⊗≡≡↑>6."/∩ε≡⎇nG⊗}D∞6/∂\]f≡/4↔_h,LV6Nl\Bεf≡LW∩ε≥dπ&F≡4ε∂π]f&O¬d∧≡}L↑2¬`VεC~ε≥lB¬`VεC"ε≡,Rπ.lLV6Nl\Bph(=v&/4@+βF%B¬`V⊗3"b@S≠eD¬`+⊗6rbε≥lB¬`V⊗s~πM∞&␈.⎇∧¬`+⊗vrε∂,QPV∞<<W∨≡\DεNvM≡&.∨MO∩π6≤∀εfN|≡G/⊗T
⊗v6}-V∂&≥⎇bπ∨M}&."∞⎇↔&F≥aPW&Tε6}nDεO'<]F2pQ!PUg≡ hUNn6↑O∧¬S∩sV
⊗ph+MV␈6↑-⊗>GF5c.NkNf⊗␈∂1PUfL\eeg;L6F∂$␈`hUM&␈G;Mε⊗␈∧∞Fzβ&>π']MfNfFFF6≥MGub⊃Q%fF-␈απ&tε#∨πO;FF6≥MC
fm⊗fgkD⊂hUM&␈B∞Mrβ∪>∞G]fm⊗fc+Mε6NMOebλQ+FF⊗␈∧π&zε&7π';Mε6NMF5fFm≥FguD⊃PUf-wBπMtβ∪∨∞O5fFm≥Fc%MfNfOkBλh+Mε⊗␈∧∞Fzβ&>π']MfNfF[FF6≥MGub⊃Q%fF-␈απ&tε#∨πO;FF6≥MC5fm⊗fgkD⊂hUM&␈B∞Mrβ∪>∞G]fm⊗fc{Mε6NMOgph+Ng≡↑≡∧β'πAQ%fG.]F(h+LF.5OO5g7.]F*ε]⊗>GDε∪ππDF/πM∧β'πOaPUf≥FN>o;FF⊗␈∧π&zε∞π']M∞6↑O∧¬S∪'∞K@*≠Mε6NMOa5gAQ%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOa5b⊃Q%fF-␈απ&tε#∨πO;FF6≥MB≥fm⊗feOOef∨!Q#β↓kKCββαkEcβε∩eecεε!5eFεβ→5KFββ!kKCββRkEcβεbeecεεuf∨!Q%fv|≥FN>o;FG↔]LWph&ε⊃5eFε∪↓5KFβ	kKCβ"kEcβ⊗2eecε⊗A5eFε∪)5KFβ1kKCβ{L7⊂h+Mf}∞M≤vw]M∞'.f←aPSβ"kEcβ&αeecε&⊃5eFε#⊃5KFβ∪→kKCβ∪BkEcβ&Reecε&a5eFε#=f>!PUfm|⊗fN⎇o5fG.]F/pQ&β→5KFβ≠↓kKCβ≠∩kEcβ6"eecε615eFε3!5KFβ≠)kKCβ≠bkEcβ6{F∨⊂Q+Fv}≥M⊗>w;Mπ↔.L←`hSεBeecεF↓5eFεC	5KFβ#⊃d∧ααααdααα∧αeecεFQ5eFεC15KFβ#=L> hUMmv∞f5⊗\\066⊗\\067\cr
\noalign{\hrule}
07⊗\\070⊗\\071⊗\\072⊗\\073⊗\\074⊗\\075⊗\\076⊗\\077\cr
\noalign{\hrule}
10⊗\\100⊗\\101⊗\\102⊗\\103⊗\\104⊗\\105⊗\\106⊗\\107\cr
\noalign{\hrule↑
11⊗\X110⊗\\111⊗\\112⊗\\113⊗\\114⊗\\115⊗\\114∩\\117\cr
Tnoalign{\hrule}
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¬c#≠'fcxZs`h*s#⊗{aβSz↓IOC'Zs#≠Nc2qk:~s#≠Nc2ssq2q∧4Uc#?BβS=↓∪≠CSnfC≠'3eak≥∞fC≠'3ecsxZbλ4*sF∪?aβ&y↓IOπ#ns#6K32qV9∞s#6K32sgpZq∧hRs#␈AβS=β⊃OCS]c#≠'fbqk≥≥c#≠'fbssx5a∧4*fC?aπ#=↓I∨βSnsF3'32cS≥∞sF3'32gcxZqλh*s#⊗{aβSz↓IOC'Zs#≠Nc2qk:~s#≠Nc2ssq2q∧4Uc#?BβS=↓∪≠CSnfC≠'3eak≥∞fC≠'3ecsxZbλ4*sF∪?aβ&y↓IOπ#ns#6K32qV9∞s#6K32sgrs∂HhQA@ZeaAA@5bqAA	2rqAβ⊂Zrqβ↓LZrc↓APZeaAAT5bqAA12rqAβ:s∂HhRs;?∞c'∨;]c#KWf+x4)βλZrqβ	@Zrc↓EDZeaAEH5bqAE→2rqA Zrqβ	TZrc↓EXZeaAE↑f≠H4*fs?π3N;;nsG∪W3↔ph)AH5bqAI↓2rqA∪λZrqβ⊃HZrc↓ILZeaAIP5bqAI)2rqA∪0Zrqβ⊃↑s∂⊂h*s;}3'∨wZs#K.c↔x4S↓LZrc↓M@ZeaAMD5bqAM⊃2rqA≠_Zrqβ→PZrc↓MTZeaAMX5bqAM=c∂H4Uc;?πfK∨;nfCKW3/p4)A!2rqA#Zrqβ!DZrc↓QHZeaAQL5bqAQ!2rqA#(Zrqβ!XJrc↓Q↑s∨⊂4*sv{π3'>sns#↔+3↔xhQATZeaAU@5bqAU	2rqA+⊂Zrqβ)LZrc↓UPZeaAUT5bqAU12rqA+:s∂HhRs;?∞c'∨;]c#KWf+x4)β0Zrqβ1@Zrc↓YDZeaAYH5bqAY→2rqA3 Zrqβ1TZrc↓YXZeaAY↑f≠H4*fs?π3N;;nsG∪W3↔ph)A\5bqA]↓2rqA;λZrqβ9HZrc↓]LZeaA]P5bqA])2rqA;0Zrqβ9↑s∂⊂h*s;}3'∨wZs#K.c↔x4S	@Zrc	A@ZeaEAD5bqEA⊃2rqEβ_Zrq↓PZrc	ATZeaEAX5bqEA=c∂H4Uc;?πfK∨;nfCKW3/p4)E	2rqEZrq	DZrc	EHZeaEEL5bqEE!2rqE(Zrq	XZrc	E↑s∨⊂4*sv{π3'>sns#↔+3↔xhQEHZeaEI@5bqEI	2rqE∪⊂Zrq⊃LZrc	IPZeaEIT5bqEI12rqE∪:s∂HhRs;?∞c'∨;]c#KWf+x4)_Zrq→@Zrc	MDZeaEMH5bqEM→1↓↓↓αZrq→TY↓α↓↓Yα↓↓↓αf≠H4*fs?π3N;;nsG∪W3↔ph)EP5bqEQ↓2rqE#λZrq!HZrc	QLZeaEQP5bqEQ)2rqE#0Zrq!↑s∂⊂h*s;}3'∨wZs#K.c↔x4S	TZrc	U@ZeaEUD5bqEU⊃2rqE+_Zrq)PZrc	UTZeaEUX5bqEU=c∂H4Uc;?πfK∨;nfCKW3/p4)E12rqE3Zrq1DZrc	YHZeaEYL5bqEY!2rqE3(Zrq1XZrc	Y↑s∨⊂4*sv{π3'>sns#↔+3↔xhQE\ZeaE]@5bqE]	2rqE;⊂Zrq9LZrc	]PZeaE]T5bqE]12rqE;:s∂Kph*s#↔+3↔xhP4*sεJs[≡['A↓
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X;∪ε[~→P∀[4∧p≥8∧~∃)Q	←pAi<@dgaβ#ns#4¬⊗f@
P∞$→4v6/↔⊂BE.~13p_tk "3ppsLhfill7\hfiLl}}
\p
gW%`@iAβ 4*SG∪W3∀hRs∪↔5csns7∪W3∃∧C↔'∨G!↓EC∧εBε&↑
FBβ to 23pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 23pt{\hfill\:u#\hfill\|}⊗\!
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\hbox to 23pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 23pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 23pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 23pt{\hfill\:u#\hfill\|}\cr
00⊗\\000⊗\\001⊗\\002⊗\\003⊗\\004⊗\\005⊗\\006⊗\\007\cr
\noalign{\hrule}
01⊗\\010⊗\\011⊗\\012⊗\\013⊗\\014⊗\\015⊗\\016⊗\\017\cr
\noalign{\hrule}
02⊗\\020⊗\\021⊗\\022⊗\\023⊗\\024⊗\\025⊗\\026⊗\\027\cr
\noalign{\hrule}
03⊗\\030⊗\\031⊗\\032⊗\\033⊗\\034⊗\\035⊗\\036⊗\\037\cr
\noalign{\hrule}
04⊗\\040⊗\\041⊗\\042⊗\\043⊗\\044⊗\\045⊗\\046⊗\\047\cr
\noalign{\hrule}
05⊗\\050⊗\\051⊗\\052⊗\\053⊗\\054⊗\\055⊗\\056⊗\\057\cr
\noalign{\hrule}
06⊗\\060⊗\\061⊗\\062⊗\\063⊗\\064⊗\\065⊗\\066⊗     \cr
\noalign{\hrule}
07⊗\\070⊗\\071⊗\\072⊗\\073⊗\\074⊗\\075⊗\\076⊗     \cr
\noalign{\hrule}
10⊗\\100⊗\\101⊗\\102⊗\\103⊗\\104⊗\\105⊗\\106⊗\\107\cr
\noalign{\hrule}
11⊗\\110⊗\\111⊗\\112⊗\\113⊗\\114⊗\\115⊗\\116⊗\\117\cr
\noalign{\hrule}
12⊗\\120⊗\\121⊗\\122⊗\\123⊗\\124⊗\\125⊗\\126⊗\\127\cr
\noalign{\hrule}
13⊗\\130⊗\\131⊗\\132⊗\\133⊗\\134⊗\\135⊗\\136⊗\\137\cr
\noalign{\hrule}
14⊗\\140⊗\\141⊗\\142⊗\\143⊗\\144⊗\\145⊗\\146⊗\\147\cr
\noalign{\hrule}
15⊗\\150⊗\\151⊗\\152⊗\\153⊗\\154⊗\\155⊗     ⊗     \cr
\noalign{\hrule}
16⊗\\160⊗\\161⊗\\162⊗\\163⊗\\164⊗\\165⊗\\166⊗\\167\cr
\noalign{\hrule}
17⊗\\170⊗\\171⊗\\172⊗\\173⊗\\174⊗\\175⊗\\176⊗\\177\cr}
\hrule}

\par\vfill\end

\noindent{\bf \ \TEX\ Standard Math Extension Fonts.}\lbrk 
The table of
128 codes on the next page
shows the form \TEX\ expects the extension ({\tt ex}) font to
have in math mode, if you use variable delimiters or the control
sequences for large operators listed later in this appendix.

\noindent{\bf 6. \TEX\ standard math symbol fonts.}\xskip The following
table of 128 codes shows the form \TEX\ expects the symbol ({\tt sy}) fonts
to have in math mode, if you use the control sequences for various special
symbols listed later in this appendix, or if you use special keys on your
terminal in math mode as explained below in subsection 8. Several positions
are undefined; they can be filled with any special characters
that might be needed in a particular job. The character in position
\¬100, which is used to negate a relation, has zero width.

\moveright26pt\vbox{
\def\\{\char'}
\hbox{\hbox to 25pt{\hfill0\hfill}\!
\hbox to 25pt{\hfill1\hfill}\!
\hbox to 25pt{\hfill2\hfill}\!
\hbox to 25pt{\hfill3\hfill}\!
\hbox to 25pt{\hfill4\hfill}\!
\hbox to 25pt{\hfill5\hfill}\!
\hbox to 25pt{\hfill6\hfill}\!
\hbox to 25pt{\hfill7\hfill}}
\vskip 4pt
\hrule
\def\|{\vrule height 10.5pt depth 4.5pt}
\halign{\hbox to 0pt{\hskip -24pt\¬#0\hfill}⊗\|
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}⊗\!
\hbox to 25pt{\hfill\:u#\hfill\|}\cr
00⊗\\000⊗\\001⊗\\002⊗\\003⊗\\004⊗\\005⊗\\006⊗\\007\cr
\noalign{\hrule}
01⊗\\010⊗\\011⊗\\012⊗\\013⊗\\014⊗\\015⊗\\016⊗\\017\cr
\noalign{\hrule}
02⊗\\020⊗\\021⊗\\022⊗\\023⊗\\024⊗\\025⊗\\026⊗\\027\cr
\noalign{\hrule}
03⊗\\030⊗\\031⊗\\032⊗\\033⊗\\034⊗\\035⊗\\036⊗\\037\cr
\noalign{\hrule}
04⊗\\040⊗\\041⊗\\042⊗\\043⊗\\044⊗\\045⊗\\046⊗\\047\cr
\noalign{\hrule|
05⊗\\050⊗\\051⊗\\052⊗\\053⊗\\054⊗\\055⊗\\056⊗\\057\cr
\noalign{\hrule}
06⊗\\06 ⊗\\061⊗\\062⊗\\063⊗\\064⊗\\06%⊗\\066⊗     \cr
\noalign{\hruLe}¬
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∞↔↔"
|bπ&Tπ≡/≡\Vv≡↑5∩rα
Mε*εM⎇Ff∂$∞6N>n4ε∂⊗T
f..L\Bε∞lDπ&F←⊃PW≡≤⎇fN7∀∞FF∂D∞FF*=ε∂⊗≤>F/↔4
⊗rπ≡\W∨&≥⎇bε∂,Tε↑/∞Dπ>OM∧π&FT
V∂&∧f}wN5`hPQ+Gε∂+Nf6NMKF.vAQ hUN>V↔≡\>FN}l,V>No:FF*λ↑6≡∂T∧≡F≡,⊗∨&↑$αEeE∨`hPQ('JεL\f∂.NEBπ&Tε⊗∞=>6f∂=∧ε≡F≡,⊗∨&↑$αEeE∀εO~∞,W≡/.lV"ε≡4π&FT∂5g≡DW≡≡≡PhV=↔⊗∞>LW↔r∞Mrπ&]MB¬eH[¬bπM↔"πMRπ∨≥\&}b
}"π∨N-⊗v:
|bε∞N
ε∞⊗↑M⊗_h,=ε∂⊗≤>F/↔4∞FF∂Df}fM}w~ε≡4εv␈AQ&
π≡'"ε|dπ&FT∞F/GD'/"∞Mε∂"
≡BεO4∩¬eH[¬bε≥n7'↔\>FN}d
v2π=⎇V*π=}'"r∧	⊗0h-⎇f*π|≥g'~∀ε⊗∞=>6f∂=∧π&z≡πε.≡$ε∂~∀ε≡F≡,⊗∨&↑$εNr∞Mε*εm≥f∞bMv∨.\]g"α≡0hV.↑7"π↑<V"ε≥dπ&F≡4π≡.nLVv≡U∀π&F]dε}vT
W/∨D∞GOεT
↔"πN⎇⊗≡*D∞FG/4¬¬eeKE∩ph*≡V/∨M≥vsR

w:εM≤Bπ&Tπ?⊗≡LW∩ε|↑Bπ&Tε⊗∞=>6f∂=∧π&z≡πε.≡$π'>≤<RεNd∞FFO1Q&&}>]V.wGthPQ+G∨..>V↔≡\>FN}l,V>No:FF*	\↔&BY]v&*
?⊗n⊗⎇DαEbE∀πph!Q%&FTF}fL≡"π≡≤⎇bαEDE∩εO4∞W≡.D'J¬JHUEb∞Mrε∞>Dε∂~∀π∨ε\=⊗∞`Q,'⊗∞=<W"nM≥6*π?≥V⊗}D∞Fzε]l6f␈<Tπε␈.M⊗}w4
v2πMRπ&←∞Bπ&≡Bε∂,Tπ&z,Rπ'≡V h.>V⊗V\>Bπ&t6/↔L≥⊗rε\≡FF.\≡FN≡≥Dε≡}nlVw&≥⎇g~r∧⊗␈*
↔6*∞<V.r∞MεO~∞↑6."≤&␈6QQ&Nr∞Mε*ε←∞εf∞l≡FN}d
v2ε
}rπ≡↑lW⊗∞D
v2πMRπ⊗↑<W↔6\Dε≡F≡,⊗∨&↑.2εNl=G.&≥lrπ&Tεf.nDε∞vD∞&N>∞Dε↔⊗≤<W~π|↑&*πO≡ε."∞⎇ε.r
lV.&\APV∂4∩πε≡.Bε}d∞FF.T∞F/GEd∧∞v}Mε/∩←ε∞o
HRπ>}.FBεm}FNvyphen but if it is enclosed by dollar signs
thus, (\$-\$) it then appears as a minus sign thus ($-$).

Two variations of the Math-Mode are used, the simple Math-Mode, used when
mathematical symbols (or equations) are to appear in running text, and the
Display Math-Mode, used when the mathematical expression iq to appear on a
separate line.  In this latter case the expression must both begin and end
With two dollar qigns
¬
\subsubsecTionbeein{The Grouping Symbols  ($\[$) and ($\} )}
	
The leFt braca ($\{$) and The rieht bpace ($\}$) abe qseD by \TAP\ to
Delimit the action o@HAIKMαK;∃β&C∃βK∞s↔¬β|∧bε.lhV∨&≡hVv/>4ε}H≡w∞=λ_smn≤[p⊗βE9r`1u`@;≤∧W?β⊂0w→⊂7s⊂≤2v0z→p⊂&*⊃l.⊂ /perators.A0∩R-Bqβπe;πgM∧∧WGε\8
∞P:42\2P:7CE12P≠pz1d~w3P(_ty1P≠pε braces, shi@
PAGC8AEJX↓C]HAα{⊂↔→;@⊂_y2V⊂≠2yz2Y⊂:7P→αh∂kd4⊂ ?$λ	M≡Y(⊂⊗→{2v)K⊂0w2λ4z⊂ #an get badly c@=]Mkgα+⊃βπv!β'O≥+∃β'v≠?7C⊗+#↔≠≤¬⊗⊗@→#"L↑\[p→λ4ryiXpπes when↓EeCG∃`
βπ⊗)β+|@λ
\=_r\α⊂ So be@]CeJ\4⊂∩¬9MkEgkα∪OW≤∧V∨&≥yf⊗.⎇→g]&T∧.vE]v"lM→f*¬?_,-{≤h∧¬↔	*/@∧¬α
The Perce@9hAgSα;9↓DRNO4λL\⎇;⊂⊂\αhp∩Aα#↔6≥lV"πMtε⊗*≥Rε.βY⊂≠pε l@%]JAgβK7∨bp4*SFK@~π=_.
α8	 @5KCMf↓iQC@ ∧ε/6↑/↔&F≥lrπε≡Bε6β{⊂⊗≠{yP )t to the @¬GikC0AK@; ∧ε}H≥~T≥_`0e`λ~∃αc';∃∧¬↔4~9{M}Y9⊗λ8∧huS a`→Yα{←'lpλ←≤≠⊂⊂[0z7`2y co@5[@↔nN2π≠h⊂⊂\82pyλ4p∞ @QQJAgα{WK∂(h ↔→>≥∧∞βtr4≠zz⊂ "ei`≥NαβSπ<XD∞α7P "e part of the @=kiakβ!β@&←∞B`!α@

\subsubsu@	`∂.>M⊗}v,X	m≥↑q~T⊂;⊂∀Yβn`≠KαsQαS∞⊃↓!∩d¬w&Nβ90→I∀␈εEβE*42H0pi@≥]P↔↔w!β@&≤ λ¬∧α.7`4imes$) i`&↓kgKHαβS :∞9ε␈:∞Mε*εLXm≡Y9⊂_v4sw≠p¬`≥hαβ?2∞L⊗↔9_<AQXεpz→y0	al, a`&↓oS@3bβ∃β,ππε@_:0↔→p∧ l@¬iKdAαK9βSF)β∪'α8λn↑|z0↔[⊂7sεBαp	QJ↓G←]iI←XAgα+GW↔v≠↔MαβKFF∞β~0∪[⊂0w2λ,.3 !lignQb]l8RT4Ph ∃@≤⎇0⊃≤zq0∪@UEgKGβ#'?;⊗+⊂≡No:FF*	nVn⊗↑ λ
=9{@⊂
⊂∧\#%)x4Ph"S#*β;G\,W$≤z1mdλ	↔∧∀λ(⊂∀\β us@∃HAS\αβSO=∧ε7ε.=_⊗bπ|∨↔5λ≥~T→Z0→≤βt being @%\⊂∀n∂Ktλ	\β0	nitigns, whepe i@PASfAβ#=β*β⊂⊗@{≠⊂↔]pr⊂ $icid↓C]HAαK9βπd¬⊗ =Y90↔≥∧¬∃Aβ∪↔π\-F/~βλ⊂⊂\β wi@1XAEJ↓KqaYα';↔ ∧εf∂LXE@∧¬α
\subsubsuBpπCGi%←]EK≥S]wπUaKe@≤∧7-<≥⊂_w2⊂)]q9q`2ipt Symbo@1`
↓∧KG/αE∃Bε∞βY⊂
⊂∧\down$)@x~∀4U##∃β/↓7πK⊗{]βπv!βS#*β∪/←pkπKK|εrε∂,Tπ/≡\@λ/(⊂∞*⊃l.⊂ 4o indicate sup@∃`O∂⊗KCSMε;⊂4U≠WO≤ε&OπN5b¬≡\Tπ&FT
6.∨M→vrε⎇`¬'O
→f*∧β8=
∧⊃[|M↑;_<dY|@⊂→2z0t[9SεEβE∩f8_y*3#~v6."[2εE

This manual's use of fonts

A word about the fonts used in this manual.
A typewriter-like style of type will be used to indicate the actual text and
\TEX\ commands that you might type on your terminal.  The \TEX\ output
will, of course, be shown as it would appear, although, on occassion, we
may have to use a different font from that used for the manual text itself to
avoid this further source of confusion.

\par\end

Here are the typewriter symbols that will be used:
$$\save1\hbox{\≡0123456789"#$%&@*+-=,.:;?!≡\}
\save2\hbox{\≡()<>≡≤≡≥[]{}≡`≡'→↑≡↓←\|/⊗≡spose/=≡∞≡\}
\eqalign{⊗\hbox{\tt ABCDEFGHIJKLMNOPQRSTUVWXYZ}\cr
⊗\hbox{\tt abcdefghijklmnopqrstuvwxyz}\cr
⊗\box1\cr
⊗\box2\cr}$$
Should some of these symbols not be available on your terminal, there are
ways to simulate them, as will be explained later.  There is one
additionad symbol that will be used in this manual to stand for a {\sl
blank space} when it is important to distinguish between a blank space
that you must actually type and spaces that normally appear in the text
describing what you do.  This symbol is:
$$\hbox{\tt\char'40}$$

{\sl Control sequences}

When a {\sl control sequence} is typed, the escape character must 
must be followed immediately by either 1) a string
of letters followed by a space, where the string of letters have been
defined either by default or by the user to specify an instruction of some
sort, or 2) a single non-alphabetic character that may be followed by a
space and that has again been defined to have some special meaning.  In
either case, \TEX\ automatically eats up any (and all) spaces that may
follow such instructions.  The use of the backslash followed immediately
by a space is a special control sequence in itself and it instructs \TEX\ to
introduce a space into the final document at this point.

We can illustrate the way {\sl control sequences} are typed by explaining
how the \TEX\ logo itself is typed.  Following a convention established by
Don Knuth, the backslash followed by the letters {\tt TEX} followed by a
space (which we can make clear in this manual by writing \\ {tt TEX
\char'40} has been defined earlier to be a {\sl control sequence} and to
mean that the letters are to be crowded together with the {\tt E} dropped
slightly.  So when this logo is to appear followed by a space, the writer
must type \\TEX\\char'40 . Remember you do not try to type {char'40} but
you do type a space in its stead.  If, on the other hand, this special
arrangement of letters is to appear, say, at the end of a sentence where
it is to be followed immediately by a period, the writer leaves out the
extra backslash space and simply types \\TEX.  where the period may be
typed either with or without an intervening space.  The omission of the
space works in this case because, by definition, non-alphabetic characters
are not allowed in multi-character {\sl control sequences}.  One must not
type a following alphabetic character without the intervening space
because the compiler would assume that this was a part of the character
string and would try to find a {\sl control sequence} that included this
additional letter.  This may be all a bit confusing, so if it is, leave it
and come back and reread this paragraph when you are trying to do
something similar.

The convention regarding extra spaces is, of course, related to
the fact that \TEX\ is usually given the task of reformatting the text and
of adjusting the space between words so as to justify the right margins
(an exception to this occurs when a special typewriter-like font is used)
The writer is normally freed of all restrictions as to the lengths of
the lines that he types and he can introduce extra spaces and extra
carriage returns as he sees fit.  Note, however, that an empty line is
normally used to signify a paragraph break so do not put them in
where not needed.

\par\end