%
% Copyright (C) 2008-2001 by Azzeddine LAZREK. All rights reserved.
%
% amexam.tex
% This file belongs to the RyDArab package.
%


% RyDArab examples for Plain TeX and LaTeX


\begin{arabyenv}
\centerline{EnaSr almkwn alrmzy fy lGQ alryaDyat alErbyQ}

\noindent $1-$ alAlfbaAyAt
\\
alHrwf alErbyQ fy alklmat, alty tAty fy nS al|lGQ alTbyEyQ, tAty
ElY alCkl altaly : \centerline{a , b , t , F , j , H , X , d , Z ,
r , z , s , C , S} \centerline{D , T , V , E , G , f , q , k , l ,
m , n , h , w , y}
\\
alHrwf alErbyQ fy alSyG alryaDyatyQ tAty ElY alCkl altaly :
\end{arabyenv}

$$a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g$$

$$ {\initial{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$

$$ {\tailed{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$

$$ {\stretched{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$

$$ {\looped{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$

$$ {\doublestruck{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$

$$ {\initialdoublestruck{a , b , j , d , o , w , z , h , T , y , k , l , m , n , W ,
e , f , s , q , r , F , x , P , p , v , g}}$$



\begin{arabyenv}
Aw aCkAl aXrY
\\
alHrwf al|latynyQ alSGyrQ hy : ${{\amlatinletter a} ,
{\amlatinletter b} , {\amlatinletter c} , \cdots }$
\\
alHrwf al|latynyQ alkbyrQ hy : ${\amlatinletter A} ,
{\amlatinletter B} , {\amlatinletter C} , \cdots$
\\
alHrwf alAGryqyQ alSGyrQ hy : $\alpha , \beta , \gamma , \cdots$
\\
alHrwf alAGryqyQ alkbyrQ hy : $\Gamma , \Delta , \Theta , \cdots$
\\
\noindent $2-$ alCarat
\\
alHrwf alErbyQ mE Carat fy almEadlat alryaDyatyQ hy :
\end{arabyenv}

%ou $$a{{}^{\prime}} , b{{}^{\prime}} , j{{}^{\prime}} , \cdots$$
$$a{{'}} , b{{'}} , j{{'}} , \cdots
\quad {\amhbox{Aw}} \quad a{{}^{\amprime}} , b{{}^{\amprime}} ,
j{{}^{\amprime}} , \cdots$$

%ou $$b{{}^{\prime}} , b{{}^{\prime\prime}} ,
%b{{}^{\prime\prime\prime}} , \cdots$$
$$b{{'}} , b{{'}{'}} , b{{'}{'}{'}} , \cdots
 \quad {\amhbox{Aw}} \quad
b{{}^{\amprime}} , b{{}^{\amprime\amprime}} ,
b{{}^{\amprime\amprime\amprime}} , \cdots$$

$${\hat b} , {\check b} , {\tilde b} , {\acute b} ,
 {\grave b} , {\dot b} , {\ddot b} , {\breve b} , {\bar b} ,
{\vec b} , {\overleftarrow{b}} , {\overrightarrow{b}}$$

$${\underline{abj}} , {\overline{abj}} ,
 {\widehat{abj}} , {\widetilde{abj}} ,
{\overleftarrow{abj}} , {\overrightarrow{abj}} , {\overbrace{abj}}
, {\underbrace{abj}}$$

\begin{arabyenv}
\noindent alHrwf al|latynyQ alSGyrQ mE CarQ hy : ${\amlatinletter
a}{{'}} , {\amlatinletter b}{{'}} , {\amlatinletter c}{{'}} ,
\cdots
 \quad {\amhbox{Aw}} \quad
{\amlatinletter a}{{}^{\amprime}} , {\amlatinletter
b}{{}^{\amprime}} , {\amlatinletter c}{{}^{\amprime}} , \cdots$
%ou ${\amlatinletter a}{{}^{\prime}} , {\amlatinmath b}{{}^{\prime}} ,
%{\amlatinletter c}{{}^{\prime}} , \cdots $
\\
alHrwf alAGryqyQ alSGyrQ mE CarQ hy : $\alpha{{'}} , \beta{{'}} ,
\gamma{{'}} , \cdots
 \quad {\amhbox{Aw}} \quad
\alpha{{}^{\amprime}} , \beta{{}^{\amprime}} ,
\gamma{{}^{\amprime}} , \cdots$
\\
\noindent $3-$ alArqam
\\
alArqam alErbyQ almGrbyQ alqdymQ hy :
%or $\amoldstylenum 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9$
% { } en LaTeX
${\amoldstylenum{0}} , {\amoldstylenum{1}} , {\amoldstylenum{2}} , {\amoldstylenum{3}} , {\amoldstylenum{4}} ,
{\amoldstylenum{5}} , {\amoldstylenum{6}} , {\amoldstylenum{7}} , {\amoldstylenum{8}} , {\amoldstylenum{9}}$
\\
alArqam alErbyQ almGrbyQ alqyasyQ hy :
%or {\amwarabnum $$0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9$$}
${\amwarabnum{0}} , {\amwarabnum{1}} , {\amwarabnum{2}} ,
{\amwarabnum{3}} , {\amwarabnum{4}} , {\amwarabnum{5}} ,
{\amwarabnum{6}} , {\amwarabnum{7}} , {\amwarabnum{8}} ,
{\amwarabnum{9}}$
\\
alArqam alErbyQ almCrqyQ hy :
%or {\amearabnum $$0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9$$}
${\amearabnum{0}} , {\amearabnum{1}} , {\amearabnum{2}} ,
{\amearabnum{3}} , {\amearabnum{4}} , {\amearabnum{5}} ,
{\amearabnum{6}} , {\amearabnum{7}} , {\amearabnum{8}} ,
{\amearabnum{9}}$
\\
alArqam alrwmanyQ bHrwf SGyrQ hy $ {1234}$ :
%%%%%%%%%\LR{\amlatinmath$\amloromnum{1234}$}
\\
alArqam alrwmanyQ bHrwf kbyrQ hy $ {1234}$ :
%%%%%%%%%\LR{\amlatinmath$\amupromnum{1234}$}
\\
\noindent $4-$ Elamat altrqym
\\
Elamat altrqym alErbyQ hy : $, \ . \ ; \ : \ ! \ ? \ - \cdots$
%or {\amarabpunct $, \ . \ ; \ : \ ! \ ? \ - \cdots$}
 $\quad {\amhbox{w}} \quad$
$\amlating$
\\
Elamat altrqym al|latynyQ hy :
%%%%\LR{\amlatinmath $, \ . \ ; \ : \ ! \ ? \ - \cdots$}
\\
\noindent $5-$ almHd|dat
\\
almHd|dat hy : $\lbrace , \langle , ( , | , [ , || , \{ , \cdots ,
\} , || , ] , | , ) , \rangle , \rbrace $
\\
\noindent $6-$ alrmwz
\\
alrmwz tAty balACkal altalyQ :
\end{arabyenv}

$$+ , - , * {\ } {\amhbox{Aw}} \times , {\ } = {\ } , \cdots$$
%or \wpercent

$$/ \quad ; \quad \% {\ } , {\ } \wpermille \quad ; \quad \epercent {\ } , {\ } \epermille {\ } , \cdots$$

$$<{\ } , {\ } > {\ } ; \quad \in {\ } , {\ } \ni {\ } ;
\quad \seqm {\amhbox{Aw}} \leqm {\ } , {\ } \leqv {\ } , {\ }
\cdots$$

$$\angle \quad ; \quad \exists {\ } , {\ } \forall {\ } , {\ } \cdots$$

$${\root{b}\of{\quad}} , {\sqrt{\quad}} \quad ; \quad {\sint_{}^{}}
{\amhbox{Aw}} {\lint_{}^{}} \quad ; \quad {\lim_{\quad}}
{\amhbox{Aw}} {\clim_{\quad}}$$

$${\ssum_{}^{}} {\amhbox{Aw}} {{\gsum_{\quad}^{}}} {\amhbox{Aw}} {\lsum_{\quad}^{}}
{\amhbox{Aw}} {\csum_{\quad}^{}} \quad ; \quad {\sprod_{}^{}}
{\amhbox{Aw}} {\gprod_{\quad}^{}} {\amhbox{Aw}}
{\lprod_{\quad}^{}} {\amhbox{Aw}} {\cprod_{\quad}^{}}$$

$${\not=} {\ } , {\ } {\not<} {\ } , {\ } {\not\in} {\ } , {\ } \cdots$$

\begin{arabyenv}
\noindent $7-$ aldalat
\end{arabyenv}

$$\sin , \cos , \tan , \cot , \sec , \csc ; \quad \arcsin ,
\arccos , \arctan , \arccot , \arcsec , \arccsc ;$$

$$\sinh , \cosh , \tanh , \coth , \sech , \csch ; {\ } \arcsinh
, \arccosh , \arctanh , \arccoth , \arcsech , \arccsch ;$$

$${\lg{}} , {\exp{}}$$

\begin{arabyenv}
\noindent $8-$ AHjam alrmwz
\\
alAHjam alFlaFQ l|lrmwz Hsb mwaqEha (Eady, As, As alAs) Aw (Eady,
dlyl, dlyl aldlyl) hy :
\\
- alAs : $b{\sp{b{\sp{b{\sp{b}}}}}}$
%%%%%%%%$\amb{\sp{\amb{\sp{\amb{\sp{\amb}}}}}}$
${{\amlatinletter
b}{\sp{{\amlatinletter b}{\sp{{\amlatinletter
b}{\sp{{\amlatinletter b}}}}}}}}$ $2{\sp{2{\sp{2{\sp{2}}}}}}$
%%%%\LR{\amearabnum$2{\sp{2{\sp{2{\sp{2}}}}}}$}
$\surd{\sp{\surd{\sp{\surd{\sp{\surd}}}}}}$
$+{\sp{+{\sp{+{\sp{+}}}}}}$ $<{\sp{<{\sp{<{\sp{<}}}}}}$
$({\sp{({\sp{({\sp{(}}}}}}$ $,{\sp{ ,{\sp{ ,{\sp{ ,}}}}}}$
$\cos{\sp{\cos{\sp{\cos{\sp{\cos}}}}}}$
\\
- aldlyl : $b{\sb{b{\sb{b{\sb{b}}}}}}$
%%%%%%%%$\amb{\sb{\amb{\sb{\amb{\sb{\amb}}}}}}$
${{\amlatinletter
b}{\sb{{\amlatinletter b}{\sb{{\amlatinletter
b}{\sb{{\amlatinletter b}}}}}}}}$ $2{\sb{2{\sb{2{\sb{2}}}}}}$
%%%%%%\LR{\amearabnum$2{\sb{2{\sb{2{\sb{2}}}}}}$}
$\surd{\sb{\surd{\sb{\surd{\sb{\surd}}}}}}$
$+{\sb{+{\sb{+{\sb{+}}}}}}$ $<{\sb{<{\sb{<{\sb{<}}}}}}$
$({\sb{({\sb{({\sb{(}}}}}}$ $,{\sb{ ,{\sb{ ,{\sb{ ,}}}}}}$
$\cos{\sb{\cos{\sb{\cos{\sb{\cos}}}}}}$
\\
alAHjam almXtlfQ l|lmHd|dat hy :
\\
%or ${\Biggr(}{\biggr(}{\Bigr(}{\bigr(}(
%){\bigl)}{\Bigl)}{\biggl)}{\Biggl)}$
${\Bigg(}{\bigg(}{\Big(}{\big(}(
 ){\big)}{\Big)}{\bigg)}{\Bigg)}$

$\quad {\amhbox{Aw}} \quad$ $

${\left[}{\left(}{\left[}{\Bigg(}{\left[}{\bigg(}
{\left[}{\Big(}{\left[}{\big(}{\left[}(
){\right]}{\big)}{\right]}{\Big)}{\right]}{\bigg)}
{\right]}{\Bigg)}{\right]}{\right)}{\right]} $
\\
alAHjam almXtlfQ l|lrmwz alm|mT|TQ hy :
\end{arabyenv}

$${\csum_{b=1}^{s}} c{{}^b} \ ; \ {\csum_{b=a-1}^{s}} c{{}^b}
 \quad {\amhbox{Aw}} \quad
{\lsum_{b=1}^{s}} c{{}^b} \ ; \ {\lsum_{b=a-1}^{s}} c{{}^b}$$

$${\ssum_{b=1}^{s}} c{{}^b} \ ; \ {\ssum\limits_{b=a-1}^{s}} c{{}^b}
 \quad {\amhbox{w}} \quad
{\gsum_{b=1}^{s}} c{{}^b} \ ; \ {\gsum_{b=a-1}^s} c{{}^b}$$

$${\cprod_{b=1}^{s}} c{{}^b} \ ; \ {\cprod_{b=a-1}^{s}} c{{}^b}
 \quad {\amhbox{Aw}} \quad
{\lprod_{b=1}^{s}} c{{}^b} \ ; \ {\lprod_{b=a-1}^{s}} c{{}^b}$$

$${\sprod_{b=1}^{s}} c{{}^b} \ ; \ {\sprod\limits_{b=a-1}^{s}} c{{}^b}
 \quad { \amhbox{w} } \quad
{\gprod_{b=1}^s} c{{}^b} \ ; \ {\gprod_{b=a-1}^s} c{{}^b}$$

$$ {\clim_{c\to 0}} c{{}^2} ; \ {\clim_{c\to +\infty}} c{{}^2}
 \quad {\amhbox{Aw}} \quad
{\lim_{c\to 0}} c{{}^2} ; \ {\lim_{c\to +\infty}} c{{}^2}$$

\begin{arabyenv}
alAHjam almXtlfQ l|lrmwz wHdha fy alsTr Aw daXl alnS hy :
\end{arabyenv}

$${\sint_{}^{}} \quad {\ssum_{}^{}} \quad {\sprod_{}^{}}$$

\centerline{${\sint_{}^{}} \quad {\ssum_{}^{}} \quad {\sprod_{}^{}}$}

\begin{arabyenv}
\noindent $9-$ mXtlfat
\\
alsaEQ : $\amtime$
\\
Asma-A alAChr alCmsyQ almGrbyQ hy :
\end{arabyenv}

$$\amlwm$$

\begin{arabyenv}
AsmaA- alAChr alCmsyQ almCrqyQ hy :
\end{arabyenv}

$$\amlem$$

\begin{arabyenv}
altaryX almylady yAty ElY alACkal altalyQ :
\end{arabyenv}

$$\amnumtoday \quad {\amhbox{Aw}} \quad \amwtoday$$

$$\amearabnum{\amnumtoday}
 \quad {\amhbox{Aw}} \quad
\amearabnum{\ametoday}$$

\newpage
\begin{arabyenv}
\centerline{AmFlQ nSwS ryaDyatyQ}

$1)$ aktb Ed|da rqm ECrath $3$ wwHdath $5$ wmAth $9$.
\\
$2)$ Akml almtsawyQ altalyQ bHyF tCyr kl nqTQ AlY rqm ma :
\end{arabyenv}

$$\cdot+(\cdot\times{10})+(\cdot\times{100})={539}$$

$$\cdot+\cdot\!\cdot+\cdots={539}$$

\begin{arabyenv}
$3)$ asrd AEDa-A almjmwEQ $\tailed{c}$ EnaSrha $c$ HyF $c$ Ed|d
zwjy mwjb ASGr mn $9$.
\end{arabyenv}

$$\tailed{c} = \{ c \ : \ (c\in T) \ {\amhbox{w}} \ c \
{\amhbox{zwjy}} \ {\amhbox{w}} \ 1 < c < 9 \}$$

\begin{arabyenv}
$4)$ byn mwDE kl nqTQ mn alnqT altalyQ dwn rsm almstwY alkrtyzy
 :
\end{arabyenv}

$$a(1,5) ; \ b(-2,-4) ; \ j(0,3) ; \ d(5,0) ; \
H(6,6) ; \ w(-6,-6) ; \ T(6,-6) ; \ y(-6,6)$$

\begin{arabyenv}
$5)$ aHsb alzawyQ $\angle abj$.
\\
$6)$ Hl almqadyr altalyQ :
\end{arabyenv}

$$6{\Bigg(}2c{\bigg(}8c-5{\Big(}2c+9{\big(}
4c+7{\big)}-5{\Big)}+3{\bigg)}{\Bigg)}$$

\amearabnum
$$6{\Bigg(}2c{\bigg(}8c-5{\Big(}2c+9{\big(}
4c+7{\big)}-5{\Big)}+3{\bigg)}{\Bigg)}$$
\amwarabnum

$$(7c + 5)(9c - 2)$$

\begin{arabyenv}
$7)$ rtb alArqam altalyQ :
\end{arabyenv}

$$7 , 5 , +{92} , -8 , {107} , {3\amlating 141}$$

{\amearabnum
$$7 , 5 , +{92} , -8 , {107} , {3{\amlatinpunct ,}141}$$
}

\begin{arabyenv}
$8)$ Hl almEadlat altalyQ :
\end{arabyenv}

$$7c + 5 = 0 \ ; \quad (1)$$

$$(2) \quad 7c + 5 = 0 \ ;$$

$$2c{{}\sp 2} - 3c + 5 = 0 \ ; \leqno (3a)$$

$$2mc{{}^2} - 3c + 5 = 0 \ . \eqno (3b)$$

\begin{arabyenv}
$9)$ Hl nVm almEadlat altalyQ :
\end{arabyenv}

$${\system{
{5c - 4s + 6}& { = 8s}\cr
{5c - 7s + 9}& { = 3}\cr
{5c - 7s + 9T}& { = {12}c}\cr }}
\eqno (1a)$$

$${\left\{}
{\offinterlineskip \openup1\jot \tabskip=0pt
plus1fil \vcenter{\halign{\tabskip=0pt
& \hfil$#${\ }& \hfil$#${\ }\cr
\amrl{&{3c}&+&{5s}&&& =&8}\cr
\amrl{&&-&{6s}&-&{4m}& =&9}\cr
\amrl{-&{5c}&&&+&{6m}& =&2}\cr}}}
{\right.}\leqno (1b)$$

\begin{arabyenv}
${10})$ adrs aldwal altalyQ :
\end{arabyenv}

$$d(c)={\cases{
 {-4c} & {{\amhbox{AZa kan}} c < 0} \cr
 {{\ }{\ }4c} & {{\amhbox{AZa kan}} c > 0} \cr
 {-2} & {{\amhbox{Gyr Zlk}}} \cr
 }}$$

$${\amnewfunc{SGr}}(c) = \cos(c{{}\sp 2}) + \sin(c)-6$$

$$d(c) = {{ {\amrl{b*9}} \over {\amrl{lc}} }} + b$$

$$d(c) = {\frac{b*9}{lc}} - b$$

$$d(c) = {\sqrt{{\frac{b*9}{c}}-1}}$$

$$d(c) = {\sqrt{{{ {\amrl{b*9}} \over {\amrl{lc}} }}}} - {\sqrt{c{{}\sp 2}}} + {\sqrt{5a}}$$

$$d(c) = 7 + {\root{3b} \of {2+{\frac{b*9}{c}}}} + 5$$

$$d(c) = {\lint\limits_{1}^{T}} c{{}^{b}} Dc +5
\quad {\amhbox{Aw}} \quad d(c) = {\sint\limits_{1}^{T}} c{{}^{b}}
Dc + 5 \quad {\amhbox{Aw}} \quad d(c) = {\sint_{1}^{T}} c{{}^{b}}
Dc + 5$$

\begin{arabyenv}
$11)$ aHsb almqadyr altalyQ :
\end{arabyenv}

$$d(c) = {\lsum_{b=1}^{s}} c{{}^{b}} + 5
\quad {\amhbox{Aw}} \quad d(c) = {\csum_{b=1}^{s}} c{{}^{b}} + 5$$

$$\quad {\amhbox{Aw}} \quad
d(c) = {\gsum_{b=1}^{s}} c{{}^{b}} + 5 \quad {\amhbox{Aw}} \quad
d(c) = {\ssum\limits_{b=1}^{s}} c{{}^{b}} + 5$$

$$d(c) = {\lprod_{b=1}^{s}} c{{}^{b}} + 5
\quad {\amhbox{Aw}} \quad d(c) = {\cprod_{b=1}^{s}} c{{}^{b}} +
5$$

$$\quad {\amhbox{Aw}} \quad
d(c) = {\gprod_{b=1}^{s}} c{{}^{b}} + 5 \quad {\amhbox{Aw}} \quad
d(c) = {\sprod\limits_{b=1}^{s}} c{{}^{b}} + 5$$

$${\lim_{c \to +\infty}} (c{^2}) + \amgta c
\quad {\amhbox{w}} \quad
{\lim_{c \to 0}} (c{^2}) + \amgta c $$

$$\quad {\amhbox{Aw}} \quad
 {\clim_{c \to +\infty}} (c{^2}) + \sin c
\quad {\amhbox{w}} \quad
{\clim_{c \to 0}} (c{^2}) + \cos c $$

\begin{arabyenv}
${12})$ aHsb mHd|dQ almSfwfQ $m$ altalyQ :
\end{arabyenv}

$$m = {\parent
{\matrix{ {1}&{2s}&{3}&{+5}\cr {4a}&{5}&{6}&{-2}\cr
{4a}&{5}&{6}&{-2}\cr}}} \quad {\amhbox{Aw}} \quad m =
{\left(}{\matrix{ {1}&{2s}&{3}&{+5}\cr {4a}&{5}&{6}&{-2}\cr
{4a}&{5}&{6}&{-2}\cr}}{\right)} \quad {\amhbox{Aw}} \quad m =
{\left[}{\matrix{ {1}&{2s}&{3}&{+5}\cr {4a}&{5}&{6}&{-2}\cr
{4a}&{5}&{6}&{-2}\cr}}{\right]}
$$

\begin{arabyenv}
${13})$ aHsb almHd|dQ altalyQ :
\end{arabyenv}

$$ m = {\left|}{\matrix{ {{\left|}
{\matrix{ {1}& {2s}\cr {4a}& {5}\cr}}
{\right|}}& {2s}& {3}& {5}\cr
{4}& {9}& {4a}& {5}\cr
{6}& {j}& {4a}& {5}\cr}}{\right|}$$

\begin{arabyenv}
${14})$ Hl|l jdwl aldalQ $d$ altaly :
\end{arabyenv}

$${{{{\vbox{\tabskip=0pt \offinterlineskip
\def\tablerule{\noalign{\hrule}}
%\halign{\vrule \ \hfil$#$\hfil \ & \ \hfil$#$\hfil \ &
%\ \hfil$#$\hfil\ & \ \hfil$#$\hfil\ & \ \hfil$#$\hfil \ &
%\vrule \ \hfil$#$\hfil\ \vrule\cr \tablerule
\halign{\strut\vrule\hfil\ $#$\ \hfil&\hfil\ $#$\ \hfil&\hfil\ $#$\ \hfil&
\hfil\ $#$\ \hfil&\hfil\ $#$\ \hfil&\vrule\hfil\ $#$\ \hfil\vrule\cr
\tablerule
\amrl{{c}&{-\infty}&&{0}&&{+\infty}}\cr \tablerule
\amrl{{d'(c)}&5&+&0&-&{-9}}\cr \tablerule
\amrl{&&&2&&}\cr
\amrl{{d(c)}&&\nwarrow&&\swarrow&}\cr
\amrl{&{-\infty}&&&&{-7}}\cr \tablerule
%height2pt\omit&\omit&\omit&\omit&\omit&\omit\cr \tablerule
\noalign{\smallskip}}}}}}}$$

\newpage
\begin{arabyenv}
\centerline{AmFlQ SyG ryaDyatyQ}
\end{arabyenv}

$$cb \ \seqm {\overbrace{b+\cdots+b}\sp{c {\ } {\amhbox{mrQ}}}}$$

$$b{^c} {\ }\leqm {\underbrace{b\times\cdots\times b}\sb{c {\ } {\amhbox{mrQ}}}}$$

$$2\uparrow c {\ } =
2{\sp{2{\sp{2{\sp{2{\sp{\cdot{\sp{\cdot{\sp{\cdot{\sp{2}}}}}}}}}}}}}}
\,{\raise9pt\vbox{\hbox{${\Bigg\}} {\ } c {\ }
{\amhbox{mrQ}}$}}}$$

$${{{{\vbox{\halign{&\quad\hfil$#$\hfil\cr
\amrl{b&=&0&1&2&3&4&5&6&7&\dots}\cr
\amrl{{2{^b}}&=&1&2&4&8&{16}&{32}&{64}&{124}&\dots}\cr}}}}}}$$

$$k{_l}{^m} {\ } = {\parent{\matrix{
{b{_{11}}}& {b{_{12}}}& \ldots& {b{_{1l}}}\cr
{b{\sb{21}}}& {b{_{22}}}& \ldots& {b{_{2l}}}\cr
{{\vdots}}& {{\vdots}}& {{\vdots}}& {{\vdots}}\cr
{b{_{m1}}}& {b{_{m2}}}& \ldots& {b{_{ml}}}\cr}}}
 \quad {\amhbox{Aw}} \quad
k{_l}{^m} {\ } = {\left(}{\matrix{
{b{_{11}}}& {b{_{12}}}& \ldots& {b{_{1l}}}\cr
{b{_{21}}}& {b{_{22}}}& \ldots& {b{_{2l}}}\cr
{{\vdots}}& {{\vdots}}& {{\vdots}}& {{\vdots}}\cr
{b{_{m1}}}& {b{_{m2}}}& \ldots& {b{_{ml}}}\cr}}
{\right)}$$

$${{{{\vbox{\tabskip=0pt \offinterlineskip
\def\tablerule{\noalign{\hrule}}
\halign{&\vrule#&\strut\quad\hfil#\hfil\quad\cr \tablerule
\amrl{&\omit&&\omit&{height2pt}}\cr \amrl{&$c$&&{$d(c)$}&}\cr
\amrl{&\omit&&\omit&{height2pt}}\cr\tablerule
\amrl{&\omit&&\omit&{height1pt}}\cr\tablerule
\amrl{&$0$&&$5$&}\cr\tablerule \amrl{&\omit&&\omit&{height2pt}}\cr
\amrl{&{$\vdots$}&&{$\vdots$}&}\cr
\amrl{&\omit&&\omit&{height2pt}}\cr\tablerule \noalign{\smallskip}
}}}}}}$$

$${{{{\vbox{\tabskip=0pt \offinterlineskip
\def\tablerule{\noalign{\hrule}}
\halign{\strut#&\vrule#\tabskip=1.5em plus 2.5em&\hfil#&
\vrule#&\hfil#\hfil&\vrule#&\hfil#& \vrule#\tabskip=0pt\cr
\tablerule
\amrl{&{\multispan5\hfil{\hbox{\araby{almbyan}}}\hfil}&&}\cr\tablerule
\amrl{&&&&{\omit\hidewidth{\hbox{\araby{alAHdaFyat}}}\hidewidth}&&&}\cr
\amrl{&{\raisebox{2ex}[0cm]{\hbox{\araby{alnqT}}}}&&{\omit\hidewidth
{\hbox{\araby{alsynyQ}}}\hidewidth}&&{\omit\hidewidth
{\hbox{\araby{alSadyQ}}}\hidewidth}&&}\cr\tablerule
\amrl{&$a$&&$5$&&$7$&&}\cr\tablerule
\amrl{&$b$&&$8$&&$9$&&}\cr\tablerule \noalign{\smallskip} }}}}}}$$

$${\lim_{c \to c{\sb{0}}}} f(c) = \ell \quad \Longleftrightarrow \quad
(\forall \varepsilon > 0) (\exists \ \alpha > 0) {\amhbox{bHyF}}
(\forall c \in D{\sb{f}}) (0 < |c-c{\sb{0}}| < \alpha \Rightarrow
|f(c)-\ell| < \varepsilon)$$


\endinput

$$
\amYpoint 0 0
\amYpoint 4 4
\amYpoint -4 -4
\amYpoint -4 4
\amYpoint 4 -4
$$

$$
\amXpoint a(0,0)
\amXpoint b(3,3)
\amXpoint c(-3,-3)
\amXpoint d(0,3)
\amXpoint d(-3,3)
\amXpoint f(3,-3)
$$
