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\chapter{Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø±ÛŒØ§Ø¶ÛŒ}


%At the end of this chapter we will return to xepersian adaption
\begin{intro}

Ø­Ø§Ù„ Ø¢Ù…Ø§Ø¯Ù‡ Ù‡Ø³ØªÛŒØ¯! Ø¯Ø± Ø§ÛŒÙ† ÙØµÙ„ Ø¨Ù‡ Ù‚ÙˆÛŒØªØ±ÛŒÙ† Ù‚Ø³Ù…Øª ØªÚ©ØŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø±ÛŒØ§Ø¶ÛŒØŒ Ø­Ù…Ù„Ù‡ Ù…ÛŒâ€ŒÚ©Ù†ÛŒÙ…. Ø§Ù…Ø§ ØªÙˆØ¬Ù‡ Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´ÛŒØ¯ØŒ Ø§ÛŒÙ† ÙØµÙ„ ÙÙ‚Ø· Ø³Ø·Ø­ Ú©Ø§Ø± Ø±Ø§ ØµÛŒÙ‚Ù„ Ù…ÛŒâ€ŒØ¯Ù‡Ø¯. Ø¨Ø§ â€ŒÙˆØ¬ÙˆØ¯ Ø§ÛŒÙ† Ú©Ù‡ Ù…Ø·Ø§Ù„Ø¨ Ø§ÛŒÙ† ÙØµÙ„ Ø¨Ø±Ø§ÛŒ Ø¨Ø³ÛŒØ§Ø±ÛŒ Ø§Ø² Ø§ÙØ±Ø§Ø¯ Ú©Ø§ÙÛŒ Ø§Ø³ØªØŒ Ø§Ú¯Ø± Ù†ØªÙˆØ§Ù†Ø³ØªÛŒØ¯ Ø¯Ø± Ø¢Ù† Ù¾Ø§Ø³Ø® Ø¨Ø¹Ø¶ÛŒ Ø§Ø² Ù†ÛŒØ§Ø²Ù‡Ø§ÛŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ø®ÙˆØ¯ Ø±Ø§ Ø¨ÛŒØ§Ø¨ÛŒØ¯ Ù†Ø§â€ŒØ§Ù…ÛŒØ¯ Ù†Ø´ÙˆÛŒØ¯. Ø¨Ù‡ Ø§Ø­ØªÙ…Ø§Ù„ Ø¨Ø³ÛŒØ§Ø± Ø²ÛŒØ§Ø¯ Ø¬ÙˆØ§Ø¨ Ø´Ù…Ø§ Ø¯Ø±  \lr{\AmS-\LaTeX{}} Ø¯Ø§Ø¯Ù‡ Ø´Ø¯Ù‡ Ø§Ø³Øª.
\end{intro}
\section{\texorpdfstring{Ú©Ù„Ø§Ù \lr{\texorpdfstring{\AmS}{AMS}-\LaTeX{}}}{Ú©Ù„Ø§Ù AMS-Latex}}
Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ (Ù¾ÛŒØ´Ø±ÙØªÙ‡)
\wi{Ø±ÛŒØ§Ø¶ÛŒ}\romanindex{mathematics} 
Ø§Ù†Ø¬Ø§Ù… Ø¯Ù‡ÛŒØ¯ØŒ Ø¨Ø§ÛŒØ¯ Ø§Ø² Ú©Ù„Ø§Ù 
\lr{\AmS-\LaTeX} 
Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ú©Ù„Ø§Ù 
\lr{\AmS-\LaTeX} 
Ù…Ø¬Ù…ÙˆØ¹Ù‡â€ŒØ§ÛŒ Ø§Ø² Ø¨Ø³ØªÙ‡â€ŒÙ‡Ø§ Ùˆ Ø·Ø¨Ù‚Ù‡â€ŒÙ‡Ø§ Ø¨Ø±Ø§ÛŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ø§Ø³Øª. Ù…Ø§ Ø¨ÛŒØ´ØªØ± Ø¨Ù‡ Ø¨Ø±Ø±Ø³ÛŒ Ø¨Ø³ØªÛ€ 
\pai{amsmath} 
Ù…ÛŒâ€ŒÙ¾Ø±Ø¯Ø§Ø²ÛŒÙ… Ú©Ù‡ Ø¬Ø²ÛŒÛŒ Ø§Ø² Ø§ÛŒÙ† Ú©Ù„Ø§Ù Ø§Ø³Øª. 
\lr{\AmS-\LaTeX} 
ØªÙˆØ³Ø· \wi{Ø§Ù†Ø¬Ù…Ù† Ø±ÛŒØ§Ø¶ÛŒ Ø¢Ù…Ø±ÛŒÚ©Ø§} ØªÙˆÙ„ÛŒØ¯ Ø´Ø¯Ù‡ Ø§Ø³Øª Ùˆ Ø¨Ù‡â€ŒØ·ÙˆØ± Ú¯Ø³ØªØ±Ø¯Ù‡ Ø¨Ø±Ø§ÛŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ù…ÙˆØ±Ø¯ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒÚ¯ÛŒØ±Ø¯. Ø®ÙˆØ¯ Ù„Ø§ØªÚ© Ø¯Ø§Ø±Ø§ÛŒ Ù…Ø­ÛŒØ·â€ŒÙ‡Ø§ÛŒÛŒ Ø§Ø¨ØªØ¯Ø§ÛŒÛŒ Ø¨Ø±Ø§ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ø§Ø³ØªØŒ Ø§Ù…Ø§ Ø§ÛŒÙ† Ù…Ø­ÛŒØ·â€ŒÙ‡Ø§ Ù…Ø­Ø¯ÙˆØ¯ Ù‡Ø³ØªÙ†Ø¯ 
(ÛŒØ§ Ø¨Ø±Ø¹Ú©Ø³: \lr{\AmS-\LaTeX} Ù†Ø§Ù…Ø­Ø¯ÙˆØ¯ Ø§Ø³Øª)
Ùˆ Ø¯Ø± Ø¨Ø¹Ø¶ÛŒ Ø­Ø§Ù„Ø§Øª Ù†Ø§Ù¾Ø§ÛŒØ¯Ø§Ø± Ù†ÛŒØ² Ù‡Ø³ØªÙ†Ø¯.

\lr{\AmS-\LaTeX} 
Ø¬Ø²ÛŒÛŒ Ø§Ø² ØªÙˆØ²ÛŒØ¹ Ù…ÙˆØ±Ø¯ Ù†ÛŒØ§Ø² Ø§Ø³Øª Ùˆ ØªÙˆØ³Ø· ØªÙ…Ø§Ù… ØªÙˆØ²ÛŒØ¹â€ŒÙ‡Ø§ÛŒ Ø§Ø®ÛŒØ± Ù„Ø§ØªÚ© Ø§Ø±Ø§Ø¦Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯.% 
\footnote{Ø§Ú¯Ø± Ø¢Ù† Ø±Ø§ Ù†Ø¯Ø§Ø±ÛŒØ¯ØŒ Ø¨Ù‡ 
  \texttt{CTAN:macros/latex/required/amslatex} Ù…Ø±Ø§Ø¬Ø¹Ù‡ Ú©Ù†ÛŒØ¯.} 
Ø¯Ø± Ø§ÛŒÙ† ÙØµÙ„ ÙØ±Ø¶ Ø¨Ø± Ø§ÛŒÙ† Ø§Ø³Øª Ú©Ù‡ \pai{amsmath} Ø¯Ø± Ø³Ø±Ø¢ØºØ§Ø² Ù†ÙˆØ´ØªØ§Ø±â€Œ ÙØ±Ø§Ø®ÙˆØ§Ù†ÛŒ Ø´Ø¯Ù‡ Ø§Ø³Øª:

\begin{code}
\verb|\usepackage{amsmath}|
\end{code}
\section{ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ ØªÙ†Ù‡Ø§}

Ø¯Ùˆ Ø±Ø§Ù‡ Ø¨Ø±Ø§ÛŒ Ú†ÛŒØ¯Ù† ÛŒÚ© \wi{ÙØ±Ù…ÙˆÙ„}\romanindex{formulae} ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯: Ø¯Ø± Ù…ØªÙ† Ø¯Ø§Ø®Ù„ ÛŒÚ© Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù 
(\wi{Ø³Ø¨Ú©â€Œ Ù…ØªÙ†ÛŒ}\Footnote{text style}\romanindex{textstyle})ØŒ 
ÛŒØ§ Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù Ù…ÛŒâ€ŒØªÙˆØ§Ù†Ø¯ Ø¨Ø±Ø§ÛŒ Ù†Ù…Ø§ÛŒØ´ Ø¬Ø¯Ø§Ú¯Ø§Ù†Ù‡ Ø´Ú©Ø³ØªÙ‡ Ø´ÙˆØ¯ 
(\wi{Ø³Ø¨Ú©â€Œ Ù†Ù…Ø§ÛŒØ´ÛŒ}\Footnote{display style}\romanindex{display style}). 
ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø±ÛŒØ§Ø¶ÛŒ {\femph Ø¯Ø±ÙˆÙ†} 
Ù…ØªÙ† \romanindex{equation} ÛŒÚ© Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù Ø¯Ø± Ù…ÛŒØ§Ù† Ø¯Ùˆ Ù†Ù…Ø§Ø¯  \texttt{\$} ÙˆØ§Ø±Ø¯ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯:


\begin{example}
Add $a$ squared and $b$ squared
to get $c$ squared. Or, using 
a more mathematical approach:
$a^2 + b^2 = c^2$
\end{example}
\begin{example}
\TeX{} is pronounced as 
$\tau\epsilon\chi$\\[5pt]
100~m$^{3}$ of water\\[5pt]
This comes from my $\heartsuit$
\end{example}

Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø¨ÛŒØ´ØªØ±ÛŒ Ø±Ø§ Ø¬Ø¯Ø§ Ø§Ø² Ø¨Ù‚ÛŒÙ‡ Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù Ø¨Ù†ÙˆÛŒØ³ÛŒØ¯ØŒ Ù…Ù†Ø§Ø³Ø¨â€ŒØªØ± Ø§Ø³Øª Ú©Ù‡ Ø¢Ù† Ø±Ø§ \femph{Ù†Ù…Ø§ÛŒØ´}
Ø¯Ù‡ÛŒØ¯ Ø¨Ù‡â€ŒØ¬Ø§ÛŒ Ø¢Ù†Ú©Ù‡ Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù Ø±Ø§ Ø¨Ø´Ú©Ù†ÛŒØ¯. Ø¨Ø±Ø§ÛŒ Ø§Ù†Ø¬Ø§Ù… Ø§ÛŒÙ† Ú©Ø§Ø± Ø§Ø² Ù…Ø­ÛŒØ· ÙØ±Ù…ÙˆÙ„ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯ Ùˆ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ Ø±Ø§ Ø¨ÛŒÙ†  \verb|\begin{equation}| Ùˆ
\verb|\end{equation}| Ù‚Ø±Ø§Ø± Ø¯Ù‡ÛŒØ¯.%
\footnote{Ø§ÛŒÙ† ÛŒÚ© ÙØ±Ù…Ø§Ù† \textsf{amsmath} Ø§Ø³Øª. Ø§Ú¯Ø± Ø¨Ù‡ Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø¯Ø³ØªØ±Ø³ÛŒ Ù†Ø¯Ø§Ø±ÛŒØ¯ Ø§Ø² Ù…Ø­ÛŒØ· \ei{displaymath} Ù…Ø±Ø¨ÙˆØ· Ø¨Ù‡ Ø®ÙˆØ¯ Ù„Ø§ØªÚ© Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.} 
Ø¢Ù†Ú¯Ø§Ù‡ Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø¨Ù‡ ÙØ±Ù…ÙˆÙ„ ÛŒÚ© Ø¨Ø±Ú†Ø³Ø¨ (\ci{label}) Ø¨Ø¯Ù‡ÛŒØ¯ Ùˆ Ø¯Ø± Ø¯ÛŒÚ¯Ø± Ù†Ù‚Ø§Ø· Ù†ÙˆØ´ØªØ§Ø±â€Œ Ø¨Ø§ ÙØ±Ù…Ø§Ù†  \ci{eqref} Ø¨Ù‡ Ø¢Ù† Ø§Ø±Ø¬Ø§Ø¹ Ø¯Ù‡ÛŒØ¯. Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø¨Ù‡ ÙØ±Ù…ÙˆÙ„ Ø§Ø³Ù… ÙˆÛŒÚ˜Ù‡â€ŒØ§ÛŒ Ø¨Ø¯Ù‡ÛŒØ¯ Ø¨Ù‡â€ŒØ¬Ø§ÛŒ Ø§ÛŒÙ†â€ŒÚ©Ø§Ø± Ø§Ø² ÙØ±Ù…Ø§Ù† \ci{tag} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ø§Ø² \ci{eqref} Ù†Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø¨Ø±Ø§ÛŒ \ci{tag} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.

\begin{example}
Add $a$ squared and $b$ squared
to get $c$ squared. Or, using
a more mathematical approach
 \begin{equation}
   a^2 + b^2 = c^2
 \end{equation}
Einstein says
 \begin{equation}
   E = mc^2 \label{clever}
 \end{equation}
He didn't say
 \begin{equation}
  1 + 1 = 3 \tag{dumb}
 \end{equation}
This is a reference to 
\eqref{clever}. 
\end{example}


Ø§Ú¯Ø± Ù†Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ù„Ø§ØªÚ© ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ Ø±Ø§ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ú©Ù†Ø¯ØŒ Ø§Ø² Ø´Ú©Ù„ Ø³ØªØ§Ø±Ù‡â€ŒØ¯Ø§Ø± Ù…Ø­ÛŒØ·  \texttt{equation} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯ØŒ \ei{equation*}ØŒ ÛŒØ§ Ø­ØªÛŒ Ø¢Ø³Ø§Ù†â€ŒØªØ±ØŒ ÙØ±Ù…ÙˆÙ„ Ø±Ø§ Ø¨ÛŒÙ† Ø¯Ùˆ Ø¹Ù„Ø§Ù…Øª  \ci{[} Ùˆ \ci{]} Ù‚Ø±Ø§Ø± Ø¯Ù‡ÛŒØ¯:\footnote{\romanindex{\textsf{amsmath} equation}
  \romanindex{\LaTeX equation} Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù† Ø¯ÙˆØ¨Ø§Ø±Ù‡ Ø§Ø² \textsf{amsmath} Ø§Ø³Øª. Ø§Ú¯Ø± Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø±Ø§ ÙØ±Ø§Ø®ÙˆØ§Ù†ÛŒ Ù†Ú©Ø±Ø¯Ù‡â€ŒØ§ÛŒØ¯ØŒ Ø§Ø² Ù…Ø­ÛŒØ· \texttt{equation} Ù…Ø±Ø¨ÙˆØ· Ø¨Ù‡ Ø®ÙˆØ¯ Ù„Ø§ØªÚ© Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ù†Ø§Ù… ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ \lr{\textsf{amsmath}/\LaTeX{}} Ù…Ù…Ú©Ù† Ø§Ø³Øª Ø¨Ù‡ Ù†Ø¸Ø± Ø¨Ø±Ø³Ø¯ Ú©Ù‡ Ú©Ù…ÛŒ Ú¯ÛŒØ¬â€ŒÚ©Ù†Ù†Ø¯Ù‡  Ù‡Ø³ØªÙ†Ø¯ØŒ ÙˆÙ„ÛŒ Ø§ÛŒÙ† ÙˆØ§Ù‚Ø¹Ø§Ù‹ ÛŒÚ© Ù…Ø´Ú©Ù„ Ø¨Ø±Ø§ÛŒ Ú©Ø³Ø§Ù†ÛŒ Ú©Ù‡ Ø§Ø² Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒÚ©Ù†Ù†Ø¯ Ù†ÛŒØ³Øª. Ø¨Ù‡ØªØ± Ø§Ø³Øª Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø±Ø§ Ø§Ø² Ø§Ø¨ØªØ¯Ø§ ÙØ±Ø§Ø®ÙˆØ§Ù†ÛŒ Ú©Ù†ÛŒØ¯ Ø²ÛŒØ±Ø§ Ù…Ù…Ú©Ù† Ø§Ø³Øª Ø¨Ø¹Ø¯Ø§Ù‹ Ù…Ø¬Ø¨ÙˆØ± Ø¨Ù‡ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ø§Ø² Ø¢Ù† Ø´ÙˆÛŒØ¯ØŒ Ùˆ Ø¢Ù†Ú¯Ø§Ù‡ Ù…Ø­ÛŒØ·â€ŒÙ‡Ø§ÛŒ ØºÛŒØ±â€Œ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ø´Ø¯Ù‡ Ø®ÙˆØ¯ Ù„Ø§ØªÚ© Ù…Ù…Ú©Ù† Ø§Ø³Øª ØªÙˆØ³Ø· Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ø´ÙˆØ¯.}
\begin{example}
Add $a$ squared and $b$ squared
to get $c$ squared. Or, using
a more mathematical approach
 \begin{equation*}
   a^2 + b^2 = c^2
 \end{equation*}
or you can type less for the
same effect:
 \[ a^2 + b^2 = c^2 \]
\end{example}

Ø¨Ù‡ ØªÙØ§ÙˆØª â€Œ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø¨ÛŒÙ† \wi{Ø³Ø¨Ú©â€Œ Ù…ØªÙ†ÛŒ}
 Ùˆ \wi{Ø³Ø¨Ú©â€Œ Ù†Ù…Ø§ÛŒØ´ÛŒ}
 ØªÙˆØ¬Ù‡ Ú©Ù†ÛŒØ¯: 
\begin{example}
This is text style: 
$\lim_{n \to \infty} 
 \sum_{k=1}^n \frac{1}{k^2} 
 = \frac{\pi^2}{6}$.
And this is display style:
 \begin{equation}
  \lim_{n \to \infty} 
  \sum_{k=1}^n \frac{1}{k^2} 
  = \frac{\pi^2}{6}
 \end{equation}
\end{example}

Ø¯Ø± Ø³Ø¨Ú©â€Œ Ù…ØªÙ†ÛŒØŒ Ø¹Ø¨Ø§Ø±Ø§Øª Ø·ÙˆÙ„Ø§Ù†ÛŒ ÛŒØ§ Ø¹Ù…ÛŒÙ‚ Ø±Ø§ Ø¯Ø±  \ci{smash} Ù…Ø­ØµÙˆØ± Ú©Ù†ÛŒØ¯. Ø§ÛŒÙ† Ú©Ø§Ø± Ù„Ø§ØªÚ© Ø±Ø§ ÙˆØ§Ø¯Ø§Ø± Ù…ÛŒâ€ŒØ³Ø§Ø²Ø¯ Ø§Ø±ØªÙØ§Ø¹ Ø¹Ø¨Ø§Ø±Øª Ø±Ø§ Ù†Ø§Ø¯ÛŒØ¯Ù‡ Ø¨Ú¯ÛŒØ±Ø¯ Ùˆ Ø¨Ø§Ø¹Ø« ÛŒÚ©Ù†ÙˆØ§Ø®Øª Ø´Ø¯Ù† ÙØ§ØµÙ„Ù‡ Ø¨ÛŒÙ† Ø®Ø·â€ŒÙ‡Ø§ Ù…ÛŒâ€ŒØ´ÙˆØ¯.

\begin{example}
A $d_{e_{e_p}}$ mathematical
expression  followed by a
$h^{i^{g^h}}$ expression. As
opposed to a smashed 
\smash{$d_{e_{e_p}}$} expression 
followed by a
\smash{$h^{i^{g^h}}$} expression.
\end{example}
\subsection{Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ}

Ù‡Ù…Ú†Ù†ÛŒÙ† ØªÙØ§ÙˆØªâ€ŒÙ‡Ø§ÛŒÛŒ Ø¨ÛŒÙ† \femph{\wi{Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ}}
 Ùˆ \femph{Ø³Ø¨Ú© Ù…ØªÙ†ÛŒ}
ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯. Ø¨Ù‡ Ø¹Ù†ÙˆØ§Ù† Ù…Ø«Ø§Ù„ Ø¯Ø± \femph{Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ}:

\begin{enumerate}

\item \romanindex{math mode spacing}\index{ÙØ§ØµÙ„Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ!Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ}
Ø¨Ø³ÛŒØ§Ø±ÛŒ Ø§Ø² ÙØ§ØµÙ„Ù‡â€ŒÙ‡Ø§ Ùˆ Ø´Ú©Ø³Øª Ø®Ø·â€ŒÙ‡Ø§ Ø¯Ø± Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ Ø¨ÛŒâ€ŒØ§Ù‡Ù…ÛŒØª Ù‡Ø³ØªÙ†Ø¯ØŒ Ø²ÛŒØ±Ø§ ØªÙ…Ø§Ù… ÙØ§ØµÙ„Ù‡â€ŒÙ‡Ø§ Ø¯Ø± Ø¹Ø¨Ø§Ø±Ø§Øª Ø±ÛŒØ§Ø¶ÛŒ ÛŒØ§ Ø¨Ù‡ Ø·ÙˆØ± Ù…Ù†Ø·Ù‚ÛŒ Ø§ÛŒØ¬Ø§Ø¯ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯ØŒ Ùˆ ÛŒØ§ Ø§ÛŒÙ† Ú©Ù‡ Ø¨Ø§ÛŒØ¯ ØªÙˆØ³Ø· ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒÛŒ Ù…Ø§Ù†Ù†Ø¯  \ci{,} Ùˆ \ci{quad} ÛŒØ§
\ci{qquad} ØªÙˆÙ„ÛŒØ¯ â€ŒØ´ÙˆÙ†Ø¯ 
( Ø¨Ø¹Ø¯Ø§Ù‹ Ø¨Ù‡ Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ Ù…ÛŒâ€ŒØ±Ø³ÛŒÙ…ØŒ Ø¨Ø®Ø´ 
\ref{sec:math-spacing}
%\LRE{\hyperref[sec:math-spacing]{5.4}} 
 Ø±Ø§ Ø¨Ø¨ÛŒÙ†ÛŒØ¯).
 
\item Ø®Ø·â€ŒÙ‡Ø§ÛŒ Ø®Ø§Ù„ÛŒ Ù…Ø¬Ø§Ø² Ù†ÛŒØ³ØªÙ†Ø¯. Ù‡Ø± ÙØ±Ù…ÙˆÙ„ ØªÙ†Ù‡Ø§ Ø¯Ø± ÛŒÚ© Ù¾Ø§Ø±Ø§Ú¯Ø±Ø§Ù Ù‚Ø±Ø§Ø± Ø¯Ø§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯.

\item Ù‡Ø± Ø­Ø±Ù Ø¨Ù‡ Ø¹Ù†ÙˆØ§Ù† Ù†Ø§Ù… ÛŒÚ© Ù…ØªØºÛŒØ± Ø¯Ø±Ù†Ø¸Ø± Ú¯Ø±ÙØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯ Ùˆ Ø¨Ù‡ Ù‡Ù…ÛŒÙ† Ù…Ù†Ø¸ÙˆØ± Ú†ÛŒØ¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø¯Ø± ÛŒÚ© ÙØ±Ù…ÙˆÙ„ Ù…ØªÙ† Ø¹Ø§Ø¯ÛŒ Ø¨Ù†ÙˆÛŒØ³ÛŒØ¯ (Ù‚Ù„Ù… Ù†Ø±Ù…Ø§Ù„ Ø§ÛŒØ³ØªØ§Ø¯Ù‡ Ùˆ ÙØ§ØµÙ„Ù‡ Ù†Ø±Ù…Ø§Ù„)
Ø¢Ù†Ú¯Ø§Ù‡ Ø¨Ø§ÛŒØ¯ Ù…ØªÙ† Ø±Ø§ Ø¨ÙˆØ³ÛŒÙ„Ù‡ ÙØ±Ù…Ø§Ù†  \verb|\text{...}| ÙˆØ§Ø±Ø¯ Ú©Ù†ÛŒØ¯ 
(Ù‡Ù…Ú†Ù†ÛŒÙ† Ø¨Ø®Ø´  
\ref{sec:fontsz}
%\LRE{\hyperref[sec:fontsz]{6.4}} 
Ø¯Ø± ØµÙØ­Ù‡  
\pageref{sec:fontsz} Ø±Ø§  Ø¨Ø¨ÛŒÙ†ÛŒØ¯).
\end{enumerate}
\begin{example}
$\forall x \in \mathbf{R}:
 \qquad x^{2} \geq 0$
\end{example}
\begin{example}
$x^{2} \geq 0\qquad
 \text{for all }x\in\mathbf{R}$
\end{example}

Ø±ÛŒØ§Ø¶ÛŒØ¯Ø§Ù†â€ŒÙ‡Ø§ Ø§Ø² Ù†Ù…Ø§Ø¯Ù‡Ø§ÛŒ Ù¾ÛŒÚ†ÛŒØ¯Ù‡â€ŒØ§ÛŒ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒÚ©Ù†Ù†Ø¯: Ù…Ù†Ø§Ø³Ø¨ Ø§Ø³Øª Ú©Ù‡ Ø¯Ø± Ø§ÛŒÙ†Ø¬Ø§ Ø§Ø² Ù‚Ù„Ù… \wi{\lr{blackboard bold}} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒÙ…ØŒ 
\romanindex{bold symbols} Ú©Ù‡ Ø¨Ø§ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ø§Ø² \ci{mathbb} Ø§Ø² Ø¨Ø³ØªÙ‡  \pai{amssymb} Ø¨Ø¯Ø³Øª Ù…ÛŒâ€ŒØ¢ÛŒØ¯.\footnote{\pai{amssymb} Ù‚Ø³Ù…ØªÛŒ Ø§Ø² Ú©Ù„Ø§Ù \lr{} Ù†ÛŒØ³ØªØŒ Ø§Ù…Ø§ Ù…Ù…Ú©Ù† Ø§Ø³Øª Ù‡Ù†ÙˆØ² Ù‚Ø³Ù…ØªÛŒ Ø§Ø² ØªÙˆØ²ÛŒØ¹ Ù„Ø§ØªÚ© Ø´Ù…Ø§ Ø¨Ø§Ø´Ø¯. ØªÙˆØ²ÛŒØ¹ Ø®ÙˆØ¯ Ø±Ø§ Ø¨Ø±Ø±Ø³ÛŒ Ú©Ù†ÛŒØ¯ ÛŒØ§ Ø¨Ù‡  \texttt{CTAN:/fonts/amsfonts/latex/} Ø¨Ø±ÙˆÛŒØ¯ Ùˆ Ø¢Ù† Ø±Ø§ Ø¯Ø±ÛŒØ§ÙØª Ú©Ù†ÛŒØ¯.}
\ifx\mathbb\undefined\else
Ø¢Ø®Ø±ÛŒÙ† Ù…Ø«Ø§Ù„ Ø¹Ø¨Ø§Ø±Øª Ø§Ø³Øª Ø§Ø²

\begin{example}
$x^{2} \geq 0\qquad
 \text{for all } x 
 \in \mathbb{R}$
\end{example}
\fi

Ø¬Ø¯ÙˆÙ„ 
\ref{mathalpha}
%\hyperref[mathalpha]{14.4}
 Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{mathalpha}
Ùˆ Ø¬Ø¯ÙˆÙ„  
\ref{mathfonts}
%\LRE{\hyperref[mathfonts]{4.6}}
Ø¯Ø± ØµÙØ­Ù‡
\pageref{mathfonts}
Ø±Ø§ Ø¨Ø±Ø§ÛŒ Ø¯ÛŒØ¯Ù† Ù‚Ù„Ù…â€ŒÙ‡Ø§ÛŒ Ø¯ÛŒÚ¯Ø± Ø±ÛŒØ§Ø¶ÛŒ Ø¨Ø¨ÛŒÙ†ÛŒØ¯.

\section{Ø³Ø§Ø®ØªÙ† Ø¨Ù„ÙˆÚ©â€ŒÙ‡Ø§ÛŒ ÙØ±Ù…ÙˆÙ„ÛŒ}

Ø¯Ø± Ø§ÛŒÙ† Ø¨Ø®Ø´ØŒ Ù…Ù‡Ù…ØªØ±ÛŒÙ† ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ù…ÙˆØ±Ø¯ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ø¯Ø± Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ø±Ø§ Ø´Ø±Ø­ Ù…ÛŒâ€ŒØ¯Ù‡ÛŒÙ…. Ø¨Ø³ÛŒØ§Ø±ÛŒ Ø§Ø² ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ø§ÛŒÙ† Ø¨Ø®Ø´ Ø§Ø­ØªÛŒØ§Ø¬ Ø¨Ù‡ 
\textsf{amsmath} Ù†Ø¯Ø§Ø±Ù†Ø¯ 
(Ø§Ú¯Ø± Ø§Ø­ØªÛŒØ§Ø¬ Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´Ù†Ø¯ØŒ ØµØ±ÛŒØ­Ø§Ù‹ Ø¨ÛŒØ§Ù† Ù…ÛŒâ€ŒØ´ÙˆØ¯)
Ø§Ù…Ø§ Ø¨Ù‡â€ŒÙ‡Ø±â€ŒØ­Ø§Ù„ Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ø±Ø§ ÙØ±Ø§Ø®ÙˆØ§Ù†ÛŒ Ú©Ù†ÛŒØ¯.


\romanindex{Greek letters}\textbf{\wi{Ø­Ø±ÙˆÙ ÛŒÙˆÙ†Ø§Ù†ÛŒ }Ú©ÙˆÚ†Ú©} 
Ø¨Ù‡â€Œ ØµÙˆØ±Øª \verb|\alpha|ØŒ  \verb|\beta|ØŒ \verb|\gamma|ØŒ \ldotsØŒ ÙˆØ§Ø±Ø¯ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯ Ùˆ Ø­Ø±ÙˆÙ Ø¨Ø²Ø±Ú¯ Ø¨Ù‡ ØµÙˆØ±Øª  \verb|\Gamma|ØŒ \verb|\Delta|ØŒ \ldots ÙˆØ§Ø±Ø¯ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯.\footnote{Ø¯Ø± Ù„Ø§ØªÚ© Ø­Ø±ÙˆÙ Ø¨Ø²Ø±Ú¯ Ø¢Ù„ÙØ§ØŒ Ø¨ØªØ§ØŒ Ùˆ ØºÛŒØ±Ù‡ ØªØ¹Ø±ÛŒÙ Ø´Ø¯Ù‡ Ù†ÛŒØ³ØªÙ†Ø¯ Ø²ÛŒØ±Ø§ Ø¨Ù‡ Ø´Ú©Ù„ \lr{A}ØŒ \lr{B}\ldots Ø¨Ù‡ Ù†Ø¸Ø± Ù…ÛŒâ€ŒØ±Ø³Ù†Ø¯. Ù‡Ù…ÛŒÙ†Ú©Ù‡ Ø±Ù…Ø²ÛŒÙ†Ù‡ Ø¬Ø¯ÛŒØ¯ Ø±ÛŒØ§Ø¶ÛŒ ØªÙ…Ø§Ù… Ø´ÙˆØ¯ØŒ Ù‡Ù…Ù‡ Ú†ÛŒØ² ØªØºÛŒÛŒØ± Ù…ÛŒâ€ŒÚ©Ù†Ø¯.}

Ø¨Ù‡ Ø¬Ø¯ÙˆÙ„  
\ref{greekletters}
%\LRE{\hyperref[greekletters]{2.4}} 
Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{greekletters} Ø¨Ø±Ø§ÛŒ Ø¯ÛŒØ¯Ù† Ù„ÛŒØ³ØªÛŒ Ø§Ø² Ø­Ø±ÙˆÙ ÛŒÙˆÙ†Ø§Ù†ÛŒ Ù†Ø¸Ø±ÛŒ Ø¨ÛŒÙ†Ø¯Ø§Ø²ÛŒØ¯.
\begin{example}
$\lambda,\xi,\pi,\theta,
 \mu,\Phi,\Omega,\Delta$
\end{example}


\textbf{ØªÙˆØ§Ù†â€ŒÙ‡Ø§ Ùˆ Ø§Ù†Ø¯ÛŒØ³â€ŒÙ‡Ø§}
Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù† ØªÙˆØ³Ø· 
\romanindex{exponent}\romanindex{subscript}\index{ØªÙˆØ§Ù†}\index{Ø§Ù†Ø¯ÛŒØ³} 
\verb|^|
%\index{\verb|^|}
 Ùˆ 
\verb|_|%\index{\verb|_|}
 Ù†ÙˆØ´Øª.
Ø¨Ø³ÛŒØ§Ø±ÛŒ Ø§Ø² ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ ØªÙ†Ù‡Ø§ Ø±ÙˆÛŒ Ø§ÙˆÙ„ÛŒÙ† Ø­Ø±Ù Ø¨Ø¹Ø¯ Ø§Ø² Ø®ÙˆØ¯Ø´Ø§Ù† ØªØ£Ø«ÛŒØ± Ø¯Ø§Ø±Ù†Ø¯ØŒ Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ ÛŒÚ© ÙØ±Ù…Ø§Ù† Ø¨Ø± Ø±ÙˆÛŒ Ú†Ù†Ø¯ Ø­Ø±Ù ØªØ£Ø«ÛŒØ± Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´Ø¯ØŒ Ø¨Ø§ÛŒØ¯ Ø¢Ù† Ø­Ø±ÙˆÙ Ø±Ø§ ØªÙˆØ³Ø·  \verb|{...}| Ø¯Ø± ÛŒÚ© Ú¯Ø±ÙˆÙ‡ Ù‚Ø±Ø§Ø± Ø¯Ù‡ÛŒØ¯.

Ø¬Ø¯ÙˆÙ„  
\ref{binaryrel}
%\LRE{\hyperref[binaryrel]{3.4}} 
Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{binaryrel} Ø´Ø§Ù…Ù„ Ø¨Ø³ÛŒØ§Ø±ÛŒ Ø§Ø² Ø¹Ù…Ù„Ú¯Ø±â€ŒÙ‡Ø§ Ù…Ø§Ù†Ù†Ø¯ $\subseteq$ Ùˆ $\perp$ Ø§Ø³Øª.

\begin{example}
$p^3_{ij} \qquad
 m_\text{Knuth} \\[5pt]
 a^x+y \neq a^{x+y}\qquad 
 e^{x^2} \neq {e^x}^2$
\end{example}



\textbf{\wi{Ø±Ø§Ø¯ÛŒÚ©Ø§Ù„}} 
ØªÙˆØ³Ø· \ci{sqrt} Ùˆ Ø±ÛŒØ´Ù‡Ù” $-n$Ø§Ù…  Ø¨Ù‡ ØµÙˆØ±Øª \LRE{\verb|\sqrt[|$n$\verb|]|} Ù†ÙˆØ´ØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ù„Ø§ØªÚ© Ø§Ù†Ø¯Ø§Ø²Ù‡Ù” Ø¹Ù„Ø§Ù…Øª Ø±Ø§Ø¯ÛŒÚ©Ø§Ù„ Ø±Ø§ Ø¨Ù‡â€ŒØ·ÙˆØ± Ø®ÙˆØ¯Ú©Ø§Ø± Ù…Ø´Ø®Øµ Ù…ÛŒâ€ŒÚ©Ù†Ø¯. Ø§Ú¯Ø± ØªÙ†Ù‡Ø§ Ø¹Ù„Ø§Ù…Øª Ø±Ø§Ø¯ÛŒÚ©Ø§Ù„ Ù…ÙˆØ±Ø¯ Ù†ÛŒØ§Ø² Ø¨Ø§Ø´Ø¯ Ø§Ø²  \verb|\surd| Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.

Ø¯Ø± Ø¬Ø¯ÙˆÙ„  
\ref{tab:arrows}
%\LRE{\hyperref[tab:arrows]{6.4}} 
Ø¯Ø± ØµÙØ­Ù‡Ù”  
\pageref{tab:arrows} Ø¯ÛŒÚ¯Ø± Ù¾ÛŒÚ©Ø§Ù†â€ŒÙ‡Ø§ Ù…Ø§Ù†Ù†Ø¯  $\hookrightarrow$ Ùˆ $\rightleftharpoons$ Ø¢ÙˆØ±Ø¯Ù‡ Ø´Ø¯Ù‡â€ŒØ§Ù†Ø¯.
\begin{example}
$\sqrt{x} \Leftrightarrow x^{1/2}
 \quad \sqrt[3]{2}
 \quad \sqrt{x^{2} + \sqrt{y}}
 \quad \surd[x^2 + y^2]$
\end{example}


\romanindex{three dots}
\romanindex{vertical dots}
\romanindex{horizontal dots}
\index{Ø³Ù‡â€ŒÙ†Ù‚Ø·Ù‡}
\index{Ø³Ù‡â€ŒÙ†Ù‚Ø·Ù‡!Ø¹Ù…ÙˆØ¯ÛŒ}
\index{Ø³Ù‡â€ŒÙ†Ù‚Ø·Ù‡!Ø§ÙÙ‚ÛŒ}
Ù…Ø¹Ù…ÙˆÙ„Ø§Ù‹ Ø§Ø² Ù†Ù‚Ø·Ù‡ Ø¨Ø±Ø§ÛŒ Ù†Ù…Ø§ÛŒØ´ Ø¯Ø§Ø¯Ù† Ø¹Ù…Ù„ Ø¶Ø±Ø¨ Ù‡Ù†Ú¯Ø§Ù… Ú©Ø§Ø± Ø¨Ø§ Ù†Ù…Ø§Ø¯â€ŒÙ‡Ø§ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯Ø› Ø¨Ø§ Ø§ÛŒÙ† ÙˆØ¬ÙˆØ¯ Ú¯Ø§Ù‡ÛŒ Ø§ÙˆÙ‚Ø§Øª Ø§Ø² Ú†Ù†Ø¯ Ù†Ù‚Ø·Ù‡ Ø¨Ø±Ø§ÛŒ Ú©Ù…Ú© Ú©Ø±Ø¯Ù† Ø¨Ù‡ Ø®ÙˆØ§Ù†Ù†Ø¯Ù‡ Ø¬Ù‡Øª Ú¯Ø±ÙˆÙ‡â€ŒØ¨Ù†Ø¯ÛŒ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† ÛŒÚ© Ù†Ù‚Ø·Ù‡ Ø¯Ø± ÙˆØ³Ø· Ø§Ø² \ci{cdot} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. \ci{cdots} Ø³Ù‡ \textbf{\wi{Ù†Ù‚Ø·Ù‡}}
Ø¯Ø± ÙˆØ³Ø· Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ø¯ Ø¯Ø±Ø­Ø§Ù„ÛŒâ€ŒÚ©Ù‡ \ci{ldots} Ù†Ù‚Ø·Ù‡â€ŒÙ‡Ø§ Ø±Ø§ Ø±ÙˆÛŒ Ø®Ø· Ú©Ø±Ø³ÛŒ Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ø¯. Ø¨Ø¹Ù„Ø§ÙˆÙ‡ØŒ  \ci{vdots} Ø¨Ø±Ø§ÛŒ Ù‚Ø±Ø§Ø± Ø¯Ø§Ø¯Ù† Ø¹Ù…ÙˆØ¯ÛŒ Ùˆ  \ci{ddots} Ø¨Ø±Ø§ÛŒ Ù‚Ø±Ø§Ø±Ø¯Ø§Ø¯Ù† Ú©Ø¬ ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ù†Ø¯. Ù…Ø«Ø§Ù„â€Œ Ø¯ÛŒÚ¯Ø±ÛŒ Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø¯Ø± Ø¨Ø®Ø´ 
\ref{sec:arraymat}
%\LRE{\hyperref[sec:arraymat]{2.4.4}}
Ø¨Ø¨ÛŒÙ†ÛŒØ¯.
\begin{example}
$\Psi = v_1 \cdot v_2
 \cdot \ldots \qquad 
 n! = 1 \cdot 2 
 \cdots (n-1) \cdot n$
\end{example}



ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ \ci{overline} Ùˆ \ci{underline} \textbf{Ø®Ø· Ø§ÙÙ‚ÛŒ}
Ø¯Ø±Ø³Øª Ø¯Ø± Ø¨Ø§Ù„Ø§ ÛŒØ§ Ù¾Ø§ÛŒÛŒÙ† Ø¹Ø¨Ø§Ø±Øª Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ù†Ø¯: 
\romanindex{horizontal line}
\index{Ø®Ø·!Ø§ÙÙ‚ÛŒ}
\index{Ø®Ø·!Ø¹Ù…ÙˆØ¯ÛŒ}
\begin{example}
$0.\overline{3} = 
 \underline{\underline{1/3}}$
\end{example}

ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ \ci{overbrace} Ùˆ \ci{underbrace}  \textbf{Ú©Ø±ÙˆØ´Ù‡Ù” Ø§ÙÙ‚ÛŒ}
Ø¯Ø± Ø¨Ø§Ù„Ø§ ÛŒØ§ Ù¾Ø§ÛŒÛŒÙ† ÛŒÚ© Ø¹Ø¨Ø§Ø±Øª Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ù†Ø¯:
\romanindex{horizontal brace} 
\index{Ø¨Ø±Ø§Ú©Øª!Ø§ÙÙ‚ÛŒ}\index{Ø§ÙÙ‚ÛŒ!Ø¨Ø±Ø§Ú©Øª} 
\begin{example}
$\underbrace{\overbrace{a+b+c}^6 
 \cdot \overbrace{d+e+f}^9}
 _\text{meaning of life} = 42$
\end{example}


\romanindex{mathematical accents}\index{Ù„Ù‡Ø¬Ù‡!Ø±ÛŒØ§Ø¶ÛŒ} 
Ø¨Ø±Ø§ÛŒ Ø§ÙØ²ÙˆØ¯Ù† Ù„Ù‡Ø¬Ù‡ Ù…Ø§Ù†Ù†Ø¯ \textbf{Ù¾ÛŒÚ©Ø§Ù† Ú©ÙˆÚ†Ú©} 
ÛŒØ§ Ø¹Ù„Ø§Ù…Øª \textbf{\wi{ØªÛŒÙ„Ø¯Ø§}} 
Ø¨Ù‡ Ù…ØªØºÛŒØ±Ù‡Ø§ØŒ ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ø§Ø±Ø§Ø¦Ù‡ Ø´Ø¯Ù‡ Ø¯Ø± Ø¬Ø¯ÙˆÙ„  
\ref{mathacc}
%\LRE{\hyperref[mathacc]{1.4}}
Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{mathacc} Ù…Ù…Ú©Ù† Ø§Ø³Øª Ù…ÙÛŒØ¯ Ø¨Ø§Ø´Ù†Ø¯. 
Ú©Ù„Ø§Ù‡ Ùˆ ØªÛŒÙ„Ø¯Ø§ Ú©Ù‡ Ø±ÙˆÛŒ Ú†Ù†Ø¯ Ø­Ø±Ù Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒÚ¯ÛŒØ±Ø¯ Ø¨Ø§  \ci{widetilde}
Ùˆ  \ci{widehat} Ø¯Ø±Ø³Øª Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ø¨Ù‡ ØªÙØ§ÙˆØª Ø¨ÛŒÙ†  Ù…Ø­Ù„ Ù‚Ø±Ø§Ø± Ú¯Ø±ÙØªÙ† \ci{hat} Ùˆ \ci{widehat}  \ci{bar} Ø¨Ø±Ø§ÛŒ Ù…ØªØºÛŒØ±Ù‡Ø§ÛŒÛŒ Ú©Ù‡ Ø¯Ø§Ø±Ø§ÛŒ Ø§Ù†Ø¯ÛŒØ³ Ù‡Ø³ØªÙ†Ø¯ ØªÙˆØ¬Ù‡ Ú©Ù†ÛŒØ¯.  Ø¹Ù„Ø§Ù…Øª  
 \verb|'|\Footnote{apostrophe}\romanindex{apostrophe}
%\index{'@\verb"|'"|}
 ØªÙˆÙ„ÛŒØ¯ Ù¾Ø±Ø§ÛŒÙ… 
\index{Ø¨ÛŒÛŒ@Ù¾Ø±Ø§ÛŒÙ…}\romanindex{prime} Ù…ÛŒâ€ŒÚ©Ù†Ø¯:
% a dash is --
\begin{example}
$f(x) = x^2 \qquad f'(x) 
 = 2x \qquad f''(x) = 2\\[5pt]
 \hat{XY} \quad \widehat{XY}
 \quad \bar{x_0} \quad \bar{x}_0$
\end{example}


\textbf{Ø¨Ø±Ø¯Ø§Ø±Ù‡Ø§}\romanindex{vectors}\index{Ø¨Ø±Ø¯Ø§Ø±Ù‡Ø§} 
Ø§ØºÙ„Ø¨ Ø¨Ø§ Ø§ÙØ²ÙˆØ¯Ù† ÛŒÚ© \wi{Ø¹Ù„Ø§Ù…Øª Ù¾ÛŒÚ©Ø§Ù†} 
Ø¨Ø± Ø±ÙˆÛŒ ÛŒÚ© Ù…ØªØºÛŒØ± Ø¨Ø¯Ø³Øª Ù…ÛŒâ€ŒØ¢ÛŒÙ†Ø¯. Ø§ÛŒÙ†â€ŒÚ©Ø§Ø± Ø±Ø§ Ø¨Ø§ ÙØ±Ù…Ø§Ù† \ci{vec} Ø§Ù†Ø¬Ø§Ù… Ù…ÛŒâ€ŒØ¯Ù‡ÛŒÙ…. Ø¯Ùˆ ÙØ±Ù…Ø§Ù† \ci{overrightarrow} Ùˆ \ci{overleftarrow} 
Ø¨Ø±Ø§ÛŒ Ù†Ø´Ø§Ù† Ø¯Ø§Ø¯Ù† Ù¾ÛŒÚ©Ø§Ù† Ø§Ø² $A$ Ø¨Ù‡ $B$ Ø¨Ù‡â€ŒÚ©Ø§Ø± Ù…ÛŒâ€ŒØ±ÙˆÙ†Ø¯:
\begin{example}
$\vec{a} \qquad
 \vec{AB} \qquad
 \overrightarrow{AB}$
\end{example}

Ù†Ø§Ù… ÛŒÚ© ØªØ§Ø¨Ø¹ Ù…Ø§Ù†Ù†Ø¯ Ù„Ú¯Ø§Ø±ÛŒØªÙ… Ø§ØºÙ„Ø¨ Ø¨Ø§ Ù‚Ù„Ù… Ø§ÛŒØ³ØªØ§Ø¯Ù‡ Ù†ÙˆØ´ØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯ØŒ Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ù„Ø§ØªÚ© ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ø²ÛŒØ± Ø±Ø§ Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† Ù†Ø§Ù… Ù…Ù‡Ù…ØªØ±ÛŒÙ† ØªÙˆØ§Ø¨Ø¹ Ø¨Ù‡â€ŒÚ©Ø§Ø± Ù…ÛŒâ€ŒØ¨Ø±Ø¯:
\romanindex{mathematical functions}\index{ØªÙˆØ§Ø¨Ø¹!Ø±ÛŒØ§Ø¶ÛŒ}

\setLR
\begin{tabular}{llllll}
\ci{arccos} &amp;  \ci{cos}  &amp;  \ci{csc} &amp;  \ci{exp} &amp;  \ci{ker}    &amp; \ci{limsup} \\
\ci{arcsin} &amp;  \ci{cosh} &amp;  \ci{deg} &amp;  \ci{gcd} &amp;  \ci{lg}     &amp; \ci{ln}     \\
\ci{arctan} &amp;  \ci{cot}  &amp;  \ci{det} &amp;  \ci{hom} &amp;  \ci{lim}    &amp; \ci{log}    \\
\ci{arg}    &amp;  \ci{coth} &amp;  \ci{dim} &amp;  \ci{inf} &amp;  \ci{liminf} &amp; \ci{max}    \\
\ci{sinh}   &amp; \ci{sup}   &amp;  \ci{tan}  &amp; \ci{tanh}&amp;  \ci{min}    &amp; \ci{Pr}     \\
\ci{sec}    &amp; \ci{sin} \\
\end{tabular}
\setRL

\begin{example}
\[\lim_{x \rightarrow 0}
 \frac{\sin x}{x}=1\]
\end{example}

Ø¨Ø±Ø§ÛŒ ØªÙˆØ§Ø¨Ø¹ÛŒ Ú©Ù‡ Ø¯Ø± Ù„ÛŒØ³Øª Ø¨Ø§Ù„Ø§ Ù‚Ø±Ø§Ø± Ù†Ø¯Ø§Ø±Ù†Ø¯ØŒ Ø§Ø² ÙØ±Ù…Ø§Ù† \ci{DeclareMathOperator}
Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ø­ØªÛŒ Ø­Ø§Ù„Øª Ø³ØªØ§Ø±Ù‡â€ŒØ¯Ø§Ø± Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ Ø¨Ø±Ø§ÛŒ ØªÙˆØ§Ø¨Ø¹ÛŒ Ú©Ù‡ Ø­Ø¯ Ø¨Ø§Ù„Ø§ ÛŒØ§ Ù¾Ø§ÛŒÛŒÙ† Ø¯Ø§Ø±Ù†Ø¯ ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯. Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ ØªÙ†Ù‡Ø§ Ø¯Ø± Ø³Ø±â€ŒØ¢ØºØ§Ø² Ø¨Ø§ÛŒØ¯ ÙØ¹Ø§Ù„ Ø´ÙˆÙ†Ø¯ Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ù…Ø«Ø§Ù„ Ø²ÛŒØ± Ø¨Ø§ÛŒØ¯ Ø¯Ø± Ø³Ø±Ø¢ØºØ§Ø² Ù‚Ø±Ø§Ø± Ø¯Ø§Ø¯Ù‡ Ø´ÙˆØ¯.
\begin{example}
%\DeclareMathOperator{\argh}{argh}
%\DeclareMathOperator*{\nut}{Nut}
\[3\argh = 2\nut_{x=1}\]
\end{example}
Ø¨Ø±Ø§ÛŒ \wi{ØªØ§Ø¨Ø¹ Ù‡Ù†Ú¯}\romanindex{modulo function}ØŒ Ø¯Ùˆ ÙØ±Ù… ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯: \ci{bmod} Ø¨Ø±Ø§ÛŒ Ø¹Ù…Ù„Ú¯Ø± Ø¯ÙˆØªØ§ÛŒÛŒ $a \bmod b$ Ùˆ  \ci{pmod} Ø¨Ø±Ø§ÛŒ Ø¹Ø¨Ø§Ø±ØªÛŒ Ø¨Ù‡ Ø´Ú©Ù„  $x\equiv a \pmod{b}$:
\begin{example}
$a\bmod b \\
 x\equiv a \pmod{b}$
\end{example}

\textbf{Ú©Ø³Ø±}
\index{Ù‚ÛŒÛŒ@Ú©Ø³Ø±}
Ø§ÛŒØ³ØªØ§Ø¯Ù‡ Ø±Ø§ Ø¨Ø§ ÙØ±Ù…Ø§Ù† \verb|{...}{...}|\ci{frac} Ù…ÛŒâ€ŒÙ†ÙˆÛŒØ³ÛŒÙ…. Ø¯Ø± Ø­Ø§Ù„Øª Ù…ØªÙ†ÛŒØŒ Ú©Ø³Ø± Ú©ÙˆÚ†Ú© Ù†ÙˆØ´ØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯ ØªØ§ Ø¯Ø± Ø§Ø±ØªÙØ§Ø¹ Ø®Ø· Ù‚Ø±Ø§Ø± Ø¨Ú¯ÛŒØ±Ø¯. Ø§ÛŒÙ† ÙØ±Ù… Ø±Ø§ Ø¯Ø± Ø³Ø¨Ú© Ù†Ù…Ø§ÛŒØ´ÛŒ Ù†ÛŒØ² Ø¨Ø§  \ci{dfrac} Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø§Ø¬Ø±Ø§ Ú©Ù†ÛŒØ¯. Ø§ØºÙ„Ø¨ ÙØ±Ù… Ú©Ø¬ 
$1/2$ Ø¨Ù‡ØªØ± Ø§Ø³ØªØŒ Ø²ÛŒØ±Ø§ Ø¨Ø±Ø§ÛŒ Ú©Ø³Ø±Ù‡Ø§ÛŒ Ú©ÙˆÚ†Ú© Ø®ÙˆØ§Ù†Ø§ØªØ± Ø§Ø³Øª:

\begin{example}
In display style:
\[3/8 \qquad \frac{3}{8} 
 \qquad \tfrac{3}{8} \]
\end{example}


\begin{example}
In text style:
$1\frac{1}{2}$~hours \qquad
$1\dfrac{1}{2}$~hours
\end{example}




 
Ø¯Ø± Ø§ÛŒÙ†Ø¬Ø§ ÙØ±Ù…Ø§Ù† \ci{partial} Ø¨Ø±Ø§ÛŒ \wi{Ù…Ø´ØªÙ‚ Ø¬Ø²Ø¦ÛŒ}\romanindex{partial derivative} Ø¨Ù‡â€ŒÚ©Ø§Ø± Ø±ÙØªÙ‡ Ø§Ø³Øª:
\begin{example}
\[\sqrt{\frac{x^2}{k+1}}\qquad
  x^\frac{2}{k+1}\qquad
  \frac{\partial^2f}
  {\partial x^2} \]
\end{example}

Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† \wi{Ø¶Ø±Ø§ÛŒØ¨ Ø¯ÙˆØ¬Ù…Ù„Ù‡â€ŒØ§ÛŒ} \romanindex{binomial coefficient} ÛŒØ§ Ú†ÛŒØ²Ù‡Ø§ÛŒÛŒ Ø´Ø¨ÛŒÙ‡ Ø§ÛŒÙ†ØŒ Ø§Ø² ÙØ±Ù…Ø§Ù†  \ci{binom} Ø§Ø² Ø¨Ø³ØªÛ€ \pai{amsmath} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯:
\begin{example}
Pascal's rule is
\begin{equation*}
 \binom{n}{k} =\binom{n-1}{k}
 + \binom{n-1}{k-1}
\end{equation*}
\end{example}

Ø¨Ø±Ø§ÛŒ \wi{Ø¹Ù…Ù„Ú¯Ø±Ù‡Ø§ÛŒ Ø¯ÙˆØªØ§ÛŒÛŒ} \romanindex{binary relations} Ù…Ù…Ú©Ù† Ø§Ø³Øª Ù‚Ø±Ø§Ø± Ø¯Ø§Ø¯Ù† Ù†Ù…Ø§Ø¯Ù‡Ø§ Ø¨Ø±â€ŒØ±ÙˆÛŒâ€ŒÙ‡Ù… Ù…ÙÛŒØ¯ Ø¨Ø§Ø´Ø¯. ÙØ±Ù…Ø§Ù†

\setLR
\ci{stackrel}\verb|{#1}{#2}|
\setRL

\noindent
Ù†Ù…Ø§Ø¯ Ø¯Ø±ÙˆÙ† \verb|#1| Ø±Ø§ Ø¨Ù‡ Ø§Ù†Ø¯Ø§Ø²Ù‡ Ù‚Ù„Ù… ØªÙˆØ§Ù† Ø±ÙˆÛŒ \verb|#2| Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ø¯ Ú©Ù‡ Ø¯Ø± Ù…Ø­Ù„ Ù…Ø¹Ù…ÙˆÙ„ Ø¢Ù† Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒÚ¯ÛŒØ±Ø¯.
\begin{example}
\begin{equation*}
 f_n(x) \stackrel{*}{\approx} 1
\end{equation*}
\end{example}

\textbf{\wi{Ø¹Ù…Ù„Ú¯Ø± Ø§Ù†ØªÚ¯Ø±Ø§Ù„}} 
Ø¨Ø§ ÙØ±Ù…Ø§Ù† \ci{int}, \textbf{\wi{Ø¹Ù…Ù„Ú¯Ø± Ø¬Ù…Ø¹}} 
Ø¨Ø§ \ci{sum}ØŒ Ùˆ \textbf{\wi{Ø¹Ù…Ù„Ú¯Ø± Ø¶Ø±Ø¨}}\romanindex{sum operator}\romanindex{integral operator}\romanindex{product operator} Ø¨Ø§ \ci{prod} ØªÙˆÙ„ÛŒØ¯ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯. Ø­Ø¯ Ø¨Ø§Ù„Ø§ Ùˆ Ù¾Ø§ÛŒÛŒÙ† Ø§ÛŒÙ† Ø¹Ù…Ù„Ú¯Ø±Ù‡Ø§ Ø¨Ø§ \verb|^| Ùˆ \verb|_| Ù…Ø§Ù†Ù†Ø¯ Ø§Ù†Ø¯ÛŒØ³ Ùˆ ØªÙˆØ§Ù† Ù†ÙˆØ´ØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯:
\begin{example}
\begin{equation*}
\sum_{i=1}^n \qquad
\int_0^{\frac{\pi}{2}} \qquad
\prod_\epsilon
\end{equation*}
\end{example}

Ø¨Ø±Ø§ÛŒ Ú©Ù†ØªØ±Ù„ Ø¨ÛŒØ´ØªØ± Ø±ÙˆÛŒ Ù…Ø­Ù„ Ù‚Ø±Ø§Ø± Ú¯Ø±ÙØªÙ† Ø§Ù†Ø¯ÛŒØ³â€ŒÙ‡Ø§ Ø¯Ø± Ø¹Ø¨Ø§Ø±Ø§Øª Ù¾ÛŒÚ†ÛŒØ¯Ù‡ØŒ  \pai{amsmath} ÙØ±Ù…Ø§Ù† \ci{substack} Ø±Ø§ Ø§Ø±Ø§Ø¦Ù‡ Ù…ÛŒâ€ŒÚ©Ù†Ø¯:
\begin{example}
\begin{equation*}
\sum^n_{\substack{0&lt;i&lt;n \\ 
        j\subseteq i}}
   P(i,j) = Q(i,j)
\end{equation*}
\end{example}


Ù„Ø§ØªÚ© Ù‡Ù…Û€ Ø§Ù†ÙˆØ§Ø¹  \textbf{\wi{Ø¨Ø±Ø§Ú©Øª}} 
Ùˆ \textbf{\wi{Ø­Ø§Ø¦Ù„}} \romanindex{braces}\romanindex{delimiters} (Ù…Ø§Ù†Ù†Ø¯ $[\;\langle\;\|\;\updownarrow$) Ø±Ø§ Ø­Ù…Ø§ÛŒØª Ù…ÛŒâ€ŒÚ©Ù†Ø¯.
Ø¨Ø±Ø§Ú©Øªâ€ŒÙ‡Ø§ÛŒ Ú¯Ø±Ø¯ Ùˆ Ù…Ø±Ø¨Ø¹ÛŒ Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¨Ø§ Ú©Ù„ÛŒØ¯ Ù…Ø±Ø¨ÙˆØ· Ø¨Ù‡ Ø®ÙˆØ¯Ø´Ø§Ù† Ù†ÙˆØ´Øª Ùˆ Ø¢Ú©ÙˆÙ„Ø§Ø¯ Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¨Ø§  \verb|\{| Ù†ÙˆØ´Øª Ø§Ù…Ø§ Ù‡Ù…Û€ Ø­Ø§Ø¦Ù„â€ŒÙ‡Ø§ Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¨Ø§ ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒÛŒ ÙˆÛŒÚ˜Ù‡ Ù†ÙˆØ´Øª (Ù…Ø§Ù†Ù†Ø¯
\verb|\updownarrow|).
\begin{example}
\begin{equation*}
{a,b,c} \neq \{a,b,c\}
\end{equation*}
\end{example}

Ø§Ú¯Ø± ÙØ±Ù…Ø§Ù† \ci{left} Ø±Ø§ Ø¯Ø± Ø§Ø¨ØªØ¯Ø§ÛŒ ÛŒÚ© Ø­Ø§Ø¦Ù„ Ú†Ù¾ØŒ Ùˆ ÙØ±Ù…Ø§Ù† \ci{right} Ø±Ø§ Ø¯Ø± Ø§Ø¨ØªØ¯Ø§ÛŒ ÛŒÚ© Ø­Ø§Ø¦Ù„ Ø±Ø§Ø³Øª Ù‚Ø±Ø§Ø± Ø¯Ù‡ÛŒÙ…ØŒ Ù„Ø§ØªÚ© Ø¨Ù‡â€ŒØ·ÙˆØ± Ø®ÙˆØ¯Ú©Ø§Ø± Ø§Ù†Ø¯Ø§Ø²Ù‡Ù” Ø­Ø§Ø¦Ù„ Ø±Ø§ ØªØµØ­ÛŒØ­ Ù…ÛŒâ€ŒÚ©Ù†Ø¯. ØªÙˆØ¬Ù‡ Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´ÛŒØ¯ Ú©Ù‡ ØªÙ…Ø§Ù… ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ \ci{left} Ø±Ø§ Ø¨Ø§ÛŒØ¯ Ø¨Ø§ ÙØ±Ù…Ø§Ù† Ù…ØªÙ†Ø§Ø¸Ø± \ci{right} Ø¨Ø¨Ù†Ø¯ÛŒØ¯. Ø§Ú¯Ø± Ø¯Ø± Ø³Ù…Øª Ø±Ø§Ø³Øª Ú†ÛŒØ²ÛŒ Ù†Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø§Ø²  \ci{right} Ù†Ø§Ù…Ø±Ø¦ÛŒ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯:
\begin{example}
\begin{equation*}
1 + \left(\frac{1}{1-x^{2}}
    \right)^3 \qquad 
\left. \ddagger \frac{~}{~}\right)
\end{equation*}
\end{example}

Ú¯Ø§Ù‡ÛŒ Ø§ÙˆÙ‚Ø§Øª Ù„Ø§Ø²Ù… Ø§Ø³Øª ØªØ§ Ø§Ù†Ø¯Ø§Ø²Ù‡Ù” Ø¯Ø±Ø³Øª ÛŒÚ© Ø­Ø§Ø¦Ù„ Ø±ÛŒØ§Ø¶ÛŒ Ø±Ø§ Ø¯Ø³ØªÛŒ ØªÙ†Ø¸ÛŒÙ… Ú©Ù†ÛŒÙ… \romanindex{mathematical delimiter}\index{Ø­Ø§Ø¦Ù„!Ø±ÛŒØ§Ø¶ÛŒ}
Ú©Ù‡ Ø¨Ø§ ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ  \ci{big}ØŒ \ci{Big}ØŒ \ci{bigg} Ùˆ 
\ci{Bigg} Ø¨Ù‡ Ø¹Ù†ÙˆØ§Ù† Ù¾ÛŒØ´ÙˆÙ†Ø¯ Ø¨ÛŒØ´ØªØ± ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ø­Ø§Ø¦Ù„ Ø§Ù…Ú©Ø§Ù†â€ŒÙ¾Ø°ÛŒØ± Ø§Ø³Øª:
\begin{example}
$\Big((x+1)(x-1)\Big)^{2}$\\
$\big( \Big( \bigg( \Bigg( \quad
\big\} \Big\} \bigg\} \Bigg\} \quad
\big\| \Big\| \bigg\| \Bigg\| \quad
\big\Downarrow \Big\Downarrow 
\bigg\Downarrow \Bigg\Downarrow$
\end{example}
 Ø¨Ø±Ø§ÛŒ Ø¯ÛŒØ¯Ù† Ù„ÛŒØ³Øª Ú©Ø§Ù…Ù„ÛŒ Ø§Ø² Ø­Ø§Ø¦Ù„â€ŒÙ‡Ø§ Ø¬Ø¯ÙˆÙ„  
\ref{tab:delimiters}
%\LRE{\hyperref[tab:delimiters]{8.4}}
Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{tab:delimiters} Ø±Ø§ Ø¨Ø¨ÛŒÙ†ÛŒØ¯. 
\section{ØªÙ†Ø¸ÛŒÙ… Ø¹Ù…ÙˆØ¯ÛŒ}
\subsection{ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ú†Ù†Ø¯Ú¯Ø§Ù†Ù‡}
\romanindex{multiple equation}\index{ÙØ±Ù…ÙˆÙ„â€Œ!Ú†Ù†Ø¯Ú¯Ø§Ù†Ù‡}

Ø¨Ø±Ø§ÛŒ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒÛŒ Ú©Ù‡ Ø¯Ø± Ú†Ù†Ø¯ Ø®Ø· Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒÚ¯ÛŒØ±Ù†Ø¯ ÛŒØ§ Ø¨Ø±Ø§ÛŒ \wi{Ø¯Ø³ØªÚ¯Ø§Ù‡ Ù…Ø¹Ø§Ø¯Ù„Ø§Øª}
 \romanindex{equation system},
Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø§Ø² Ù…Ø­ÛŒØ· \ei{align} Ùˆ \verb|align*| Ø¨Ù‡ Ø¬Ø§ÛŒ  \texttt{equation} Ùˆ \texttt{equation*} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.\footnote{Ù…Ø­ÛŒØ·  \ei{align} Ø§Ø² Ø¨Ø³ØªÛ€  \textsf{amsmath} Ø§Ø³Øª. Ù…Ø­ÛŒØ· Ù…Ø´Ø§Ø¨Ù‡ Ø¨Ù‡  Ø§ÛŒÙ† Ù…Ø­ÛŒØ· Ø¯Ø± Ø®ÙˆØ¯ Ù„Ø§ØªÚ© Ø¨Ø§ Ø¹Ù†ÙˆØ§Ù† \ei{eqnarray} ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯ØŒ Ø§Ù…Ø§ Ø¹Ù…ÙˆÙ…Ø§Ù‹ ØªÙˆØµÛŒÙ‡ Ù†Ù…ÛŒâ€ŒØ´ÙˆØ¯ Ø²ÛŒØ±Ø§ Ù…Ú©Ø§Ù† Ùˆ Ø¨Ø±Ú†Ø³Ø¨ Ø¢Ù† Ù¾Ø§ÛŒØ¯Ø§Ø± Ù†ÛŒØ³Øª.} 
Ø¨Ø§ \ei{align} Ù‡Ø± Ø®Ø· Ù…Ø¹Ø§Ø¯Ù„Ù‡ ÛŒÚ© Ø´Ù…Ø§Ø±Ù‡ Ù…ÛŒâ€ŒÚ¯ÛŒØ±Ø¯. \verb|align*| Ù‡ÛŒÚ† Ú†ÛŒØ² Ø±Ø§ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ù†Ù…ÛŒâ€ŒÚ©Ù†Ø¯.

Ù…Ø­ÛŒØ· \ei{align} ÛŒÚ© Ù…Ø¹Ø§Ø¯Ù„Ù‡ Ø±Ø§  Ù¾ÛŒØ±Ø§Ù…ÙˆÙ† Ø¹Ù„Ø§Ù…Øª \verb|&amp;| Ú¯Ø±Ø¯ Ù…ÛŒâ€ŒÚ©Ù†Ø¯.
ÙØ±Ù…Ø§Ù† \verb|\\| Ø®Ø·â€ŒÙ‡Ø§ Ø±Ø§ Ù…ÛŒâ€ŒØ´Ú©Ù†Ø¯. Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ ÛŒÚ© Ù…Ø¹Ø§Ø¯Ù„Ù‡ Ø±Ø§ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ù†Ú©Ù†ÛŒØ¯ Ø§Ø² ÙØ±Ù…Ø§Ù† \ci{nonumber} Ø¨Ø±Ø§ÛŒ Ø­Ø°Ù Ø´Ù…Ø§Ø±Ù‡Ù” Ø¢Ù† Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù† Ø¨Ø§ÛŒØ¯ \femph{Ù‚Ø¨Ù„}
Ø§Ø² \verb|\\| Ù‚Ø±Ø§Ø± Ø¯Ø§Ø¯Ù‡ Ø´ÙˆØ¯:
\begin{example}
\begin{align}
f(x) &amp;= (a+b)(a-b) \label{1}\\
     &amp;= a^2-ab+ba-b^2  \\ 
     &amp;= a^2+b^2 \tag{wrong}
\end{align}
This is a reference to \eqref{1}.
\end{example}

\index{ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø·ÙˆÙ„Ø§Ù†ÛŒ}\romanindex{long equations} 
\textbf{ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø·ÙˆÙ„Ø§Ù†ÛŒ} 
Ø¨Ù‡ ØµÙˆØ±Øª Ø®ÙˆØ¯Ú©Ø§Ø±  Ø´Ú©Ø³ØªÙ‡ Ù†Ù…ÛŒâ€ŒØ´ÙˆÙ†Ø¯. Ù†ÙˆÛŒØ³Ù†Ø¯Ù‡ Ø¨Ø§ÛŒØ¯ Ù…Ø´Ø®Øµ Ú©Ù†Ø¯ Ú©Ø¬Ø§ Ø¨Ø§ÛŒØ¯ Ø´Ú©Ø³ØªÙ‡ Ø´ÙˆÙ†Ø¯ Ùˆ ØªÙˆØ±ÙØªÚ¯ÛŒ Ù…Ù†Ø§Ø³Ø¨ Ø±Ø§ Ù…Ø´Ø®Øµ Ú©Ù†Ø¯:
\begin{example}
\begin{align}
f(x) &amp;= 3x^5 + x^4 + 2x^3 
                \nonumber \\
     &amp;\qquad + 9x^2 + 12x + 23 \\
     &amp;= g(x) - h(x)
\end{align}
\end{example}
Ø¨Ø³ØªÛ€ \pai{amsmath} Ú†Ù†Ø¯ Ù…Ø­ÛŒØ· Ù…ÙÛŒØ¯ Ø¯ÛŒÚ¯Ø± Ø±Ø§ Ù†ÛŒØ² Ø¯Ø± Ø¨Ø± Ø¯Ø§Ø±Ø¯: \verb|flalign|ØŒ
\verb|gather|ØŒ \verb|multline| Ùˆ \verb|split|. Ø¨Ø±Ø§ÛŒ Ø§Ø·Ù„Ø§Ø¹Ø§Øª Ø¨ÛŒØ´ØªØ± Ø¨Ù‡ Ø±Ø§Ù‡Ù†Ù…Ø§ÛŒ Ø§ÛŒÙ† Ø¨Ø³ØªÙ‡ Ù…Ø±Ø§Ø¬Ø¹Ù‡ Ú©Ù†ÛŒØ¯.
\subsection{Ø¢Ø±Ø§ÛŒÙ‡ Ùˆ Ù…Ø§ØªØ±ÛŒØ³} \label{sec:arraymat}

Ø¨Ø±Ø§ÛŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ø¢Ø±Ø§ÛŒÙ‡â€ŒÙ‡Ø§ Ø§Ø² Ù…Ø­ÛŒØ· \ei{array} Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯. Ø§ÛŒÙ† Ù…Ø­ÛŒØ· Ø´Ø¨ÛŒÙ‡ Ù…Ø­ÛŒØ·  \texttt{tabular} Ø§Ø³Øª. ÙØ±Ù…Ø§Ù† \verb|\\| Ø¨Ø±Ø§ÛŒ Ø´Ú©Ø³ØªÙ† Ø®Ø·â€ŒÙ‡Ø§ Ø¨Ù‡â€ŒÚ©Ø§Ø± Ù…ÛŒâ€ŒØ±ÙˆØ¯:
\begin{example}
\begin{equation*}
 \mathbf{X} = \left( 
  \begin{array}{ccc}
   x_1 &amp; x_2 &amp; \ldots \\
   x_3 &amp; x_4 &amp; \ldots \\
   \vdots &amp; \vdots &amp; \ddots
  \end{array} \right)
\end{equation*}
\end{example}


Ø§Ø² Ù…Ø­ÛŒØ· \ei{array} Ù‡Ù…Ú†Ù†ÛŒÙ† Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† 
\romanindex{piecewise function}\wi{ØªÙˆØ§Ø¨Ø¹ Ú†Ù†Ø¯â€ŒØ¶Ø§Ø¨Ø·Ù‡} 
ØªÙˆØ³Ø· ÛŒÚ© \verb|.| Ø¨Ù‡ Ø¹Ù†ÙˆØ§Ù† ÛŒÚ© Ø­Ø§Ø¦Ù„ Ø±Ø§Ø³Øª Ù†Ø§Ù…Ø±Ø¦ÛŒ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯:\footnote{Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø®ÛŒÙ„ÛŒ Ø§Ø² Ø§ÛŒÙ† ÙØ±Ù… Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯ Ù…Ø­ÛŒØ· \ei{cases} Ø§Ø² Ø¨Ø³ØªÛ€ 
  \textsf{amsmath} Ú©Ø§Ø± Ø±Ø§ Ø¨Ø³ÛŒØ§Ø± Ø±Ø§Ø­Øª Ù…ÛŒâ€ŒÚ©Ù†Ø¯ Ùˆ Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ø§Ø±Ø²Ø´ Ù†Ú¯Ø§Ù‡ Ú©Ø±Ø¯Ù† Ø±Ø§ Ø¯Ø§Ø±Ø¯.}  
\begin{example}
\begin{equation*}
|x| = \left\{
 \begin{array}{rl}
  -x &amp; \text{if } x &lt; 0\\
   0 &amp; \text{if } x = 0\\
   x &amp; \text{if } x &gt; 0
 \end{array} \right.
\end{equation*}
\end{example}



\ei{array} Ø±Ø§ Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† Ù…Ø§ØªØ±ÛŒØ³â€ŒÙ‡Ø§ \index{Ù…Ø§ØªØ±ÛŒØ³}\romanindex{matrix} Ù†ÛŒØ² Ø¨Ù‡â€ŒÚ©Ø§Ø± Ø¨Ø±Ø¯ØŒ Ø§Ù…Ø§ 
\pai{amsmath} Ø±Ø§Ù‡â€Œ Ø­Ù„ Ø¨Ù‡ØªØ±ÛŒ Ø±Ø§ ØªÙˆØ³Ø· Ù…Ø­ÛŒØ· \ei{matrix} Ù¾ÛŒØ´Ù†Ù‡Ø§Ø¯ Ù…ÛŒâ€ŒÚ©Ù†Ø¯. Ø´Ø´ Ù†Ø³Ø®Ù‡ Ø§Ø² Ø¢Ù† Ø¨Ø§ Ø­Ø§Ø¦Ù„â€ŒÙ‡Ø§ÛŒ Ù…Ø®ØªÙ„Ù ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯: \ei{matrix}
(Ø®Ø§Ù„ÛŒ)ØŒ \ei{pmatrix} $($ØŒ \ei{bmatrix} $[$ØŒ \ei{Bmatrix} $\{$ØŒ \ei{vmatrix} $\vert$ Ùˆ
\ei{Vmatrix} $\Vert$. Ø¨Ø§ \ei{array} Ù„Ø§Ø²Ù… Ù†ÛŒØ³Øª ØªØ¹Ø¯Ø§Ø¯ Ø³ØªÙˆÙ†â€ŒÙ‡Ø§ Ø±Ø§ Ù…Ø´Ø®Øµ Ú©Ù†ÛŒØ¯. Ø¨ÛŒØ´ØªØ±ÛŒÙ† ØªØ¹Ø¯Ø§Ø¯ Ø³ØªÙˆÙ† Û±Û° 
Ø§Ø³Øª Ø§Ù…Ø§ Ù‚Ø§Ø¨Ù„ ØªØºÛŒÛŒØ± Ø§Ø³Øª 
(Ù‡Ø±Ú†Ù†Ø¯ Ù…Ø¹Ù…ÙˆÙ„Ø§Ù‹ Ø¨ÛŒØ´ØªØ± Ø§Ø² Û±Û° Ø³ØªÙˆÙ† Ù„Ø§Ø²Ù… Ù†ÛŒØ³Øª!).
\begin{example}
\begin{equation*}
 \begin{matrix} 
   1 &amp; 2 \\
   3 &amp; 4 
 \end{matrix} \qquad
 \begin{bmatrix} 
   1 &amp; 2 &amp; 3 \\
   4 &amp; 5 &amp; 6 \\ 
   7 &amp; 8 &amp; 9
 \end{bmatrix}
\end{equation*}
\end{example}


\section{ÙØ§ØµÙ„Ù‡ Ø¯Ø± Ù…Ø­ÛŒØ· Ø±ÛŒØ§Ø¶ÛŒ}\label{sec:math-spacing}

\romanindex{math spacing}\index{ÙØ§ØµÙ„Ù‡Ù” Ø±ÛŒØ§Ø¶ÛŒ} 
Ø§Ú¯Ø± ÙØ§ØµÙ„Ù‡Ù” Ø§Ù†ØªØ®Ø§Ø¨ Ø´Ø¯Ù‡ ØªÙˆØ³Ø· Ù„Ø§ØªÚ© Ø¯Ø± ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ Ù…Ù†Ø§Ø³Ø¨ Ù†ÛŒØ³ØªØŒ Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¢Ù† Ø±Ø§ Ø¨Ø§ ÙØ±Ù…Ø§Ù†â€ŒÙ‡Ø§ÛŒÛŒ ØªØµØ­ÛŒØ­ Ú©Ø±Ø¯: \ci{,} Ø¨Ø±Ø§ÛŒ
$\frac{3}{18}\:\textrm{quad}$ (\demowidth{0.166em})ØŒ \ci{:} Ø¨Ø±Ø§ÛŒ $\frac{4}{18}\:
\textrm{quad}$ (\demowidth{0.222em}) Ùˆ  \ci{;} Ø¨Ø±Ø§ÛŒ $\frac{5}{18}\:
\textrm{quad}$ (\demowidth{0.277em}).  Ø­Ø±Ù ÙØ±Ø§Ø± \verb*|\ | ØªÙˆÙ„ÛŒØ¯ ÛŒÚ© ÙØ§ØµÙ„Ù‡ Ø¨ÛŒÙ†  \ci{quad}
(\demowidth{1em}) Ùˆ \ci{qquad} (\demowidth{2em}) Ù…ÛŒâ€ŒÚ©Ù†Ø¯. Ø§Ù†Ø¯Ø§Ø²Ù‡Ù” 
\ci{quad} Ù…ØªÙ†Ø§Ø¸Ø± Ø¨Ø§ Ø¹Ø±Ø¶ Ø­Ø±Ù \lr{`M'} Ø§Ø² Ø§ÛŒÙ† Ù‚Ù„Ù… Ø¬Ø§Ø±ÛŒ Ø§Ø³Øª.  \verb|\!|
%\cih{"!} 
ØªÙˆÙ„ÛŒØ¯ ÛŒÚ© ÙØ§ØµÙ„Ù‡Ù” Ù…Ù†ÙÛŒ Ø¨Ù‡ Ø§Ù†Ø¯Ø§Ø²Ù‡Ù”  $-\frac{3}{18}\:\textrm{quad}$ ($-$\demowidth{0.166em}) Ù…ÛŒâ€ŒÚ©Ù†Ø¯.

ØªÙˆØ¬Ù‡ Ú©Ù†ÛŒØ¯ \lr{`d'} Ø¯Ø± Ø¹Ù…Ù„ÛŒØ§Øª Ø¯ÛŒÙØ±Ø§Ù†Ø³ÛŒÙ„ Ø¨Ù‡ Ø®ÙˆØ¨ÛŒ Ø¯Ø± Ù‚Ù„Ù… Ø§ÛŒØ³ØªØ§Ø¯Ù‡ Ù†ÙˆØ´ØªÙ‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯:
\begin{example}
\begin{equation*}
 \int_1^2 \ln x \mathrm{d}x \qquad
 \int_1^2 \ln x \,\mathrm{d}x
\end{equation*}
\end{example}


Ø¯Ø± Ù…Ø«Ø§Ù„ Ø¨Ø¹Ø¯ØŒ ØªØ§Ø¨Ø¹ Ø¬Ø¯ÛŒØ¯ \ci{ud} Ø±Ø§ ØªØ¹Ø±ÛŒÙ Ù…ÛŒâ€ŒÚ©Ù†ÛŒÙ… Ú©Ù‡ Ù†Ù…Ø§Ø¯ $\,\mathrm{d}$ Ø±Ø§ ØªÙˆÙ„ÛŒØ¯ Ù…ÛŒâ€ŒÚ©Ù†Ø¯ (Ø¨Ù‡ ÙØ§ØµÙ„Ù‡Ù”  
\demowidth{0.166em}
Ù‚Ø¨Ù„ Ø§Ø² 
$\text{d}$ ØªÙˆØ¬Ù‡ Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´ÛŒØ¯)ØŒ
Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ù„Ø§Ø²Ù… Ù†ÛŒØ³Øª Ù‡Ø±Ø¨Ø§Ø± Ø¢Ù† Ø±Ø§ Ø¨Ù†ÙˆÛŒØ³ÛŒÙ…. ÙØ±Ù…Ø§Ù†  \ci{newcommand} Ø¯Ø± Ø³Ø±Ø¢ØºØ§Ø² Ø¢ÙˆØ±Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯.
\begin{example}
\newcommand{\ud}{\,\mathrm{d}}

\begin{equation*}
 \int_a^b f(x)\ud x 
\end{equation*}
\end{example}

Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø§Ù†ØªÚ¯Ø±Ø§Ù„ Ú†Ù†Ø¯Ú¯Ø§Ù†Ù‡ Ø±Ø§ Ø¨Ù†ÙˆÛŒØ³ÛŒØ¯ØŒ Ø®ÙˆØ§Ù‡ÛŒØ¯ Ø¯ÛŒØ¯ Ú©Ù‡ ÙØ§ØµÙ„Ù‡ Ø¨ÛŒÙ† Ø§Ù†ØªÚ¯Ø±Ø§Ù„â€ŒÙ‡Ø§ Ù†Ø§Ù…Ø·Ø¨ÙˆØ¹ Ø§Ø³Øª. Ù…ÛŒâ€ŒØªÙˆØ§ÛŒØ¯ Ø§ÛŒÙ† ÙØ§ØµÙ„Ù‡ Ø±Ø§ Ø¨Ø§ ÙØ±Ù…Ø§Ù†  \ci{!}
%\cih{"!}
 ØªØºÛŒÛŒØ± Ø¯Ù‡ÛŒØ¯ØŒ Ø§Ù…Ø§ Ø¨Ø³ØªÛ€ 
\pai{amsmath}
 Ø±Ø§Ù‡ Ø­Ù„ Ø³Ø§Ø¯Ù‡â€ŒØªØ±ÛŒ Ø¨Ø±Ø§ÛŒ Ø§ÛŒÙ†â€ŒÚ©Ø§Ø± Ø¯Ø§Ø±Ø¯ Ú©Ù‡ Ø¹Ø¨Ø§Ø±Øª Ø§Ø³Øª Ø§Ø²  
\ci{iint}ØŒ \ci{iiint}ØŒ \ci{iiiint}ØŒ  Ùˆ \ci{idotsint}.

\begin{example}
\newcommand{\ud}{\,\mathrm{d}}

\[ \int\int f(x)g(y) 
                  \ud x \ud y \]
\[ \int\!\!\!\int 
         f(x)g(y) \ud x \ud y \]
\[ \iint f(x)g(y) \ud x \ud y \]
\end{example}

Ø¨Ø±Ø§ÛŒ Ø§Ø·Ù„Ø§Ø¹Ø§Øª Ø¨ÛŒØ´ØªØ± Ø¨Ù‡ Ø±Ø§Ù‡Ù†Ù…Ø§ÛŒ Ø§Ù„Ú©ØªØ±ÙˆÙ†ÛŒÚ©ÛŒ  \texttt{testmath.tex} Ø§Ø² \lr{\AmS-\LaTeX} ÛŒØ§ ÙØµÙ„ Û¸ Ø§Ø² \companion{} Ù…Ø±Ø§Ø¬Ø¹Ù‡ Ú©Ù†ÛŒØ¯.
\subsection{Ø§Ø´Ø¨Ø§Ø­}

ÙˆÙ‚ØªÛŒ ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ù…Ø±ØªØ¨ Ø¹Ù…ÙˆØ¯ÛŒ Ø´Ø§Ù…Ù„  \verb|^| Ùˆ  \verb|_| Ù…ÛŒâ€ŒÙ†ÙˆÛŒØ³ÛŒØ¯ØŒ Ú¯Ø§Ù‡ÛŒ Ø§ÙˆÙ‚Ø§Øª Ù„Ø§ØªÚ© Ø®ÛŒÙ„ÛŒ Ú©Ù…Ú© Ù†Ù…ÛŒâ€ŒÚ©Ù†Ø¯. Ø¨Ø§ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ø§Ø² ÙØ±Ù…Ø§Ù†  \ci{phantom} Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ ÙØ¶Ø§ÛŒÛŒ Ø¨Ø±Ø§ÛŒ Ø­Ø±ÙÛŒ Ú©Ù‡ Ù†Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ Ø¯Ø± Ø®Ø±ÙˆØ¬ÛŒ Ø¸Ø§Ù‡Ø± Ø´ÙˆØ¯ Ø§ÛŒØ¬Ø§Ø¯ Ú©Ù†ÛŒØ¯. Ø±Ø§Ø­Øªâ€ŒØªØ±ÛŒÙ† Ø±Ø§Ù‡ Ø¨Ø±Ø§ÛŒ ÙÙ‡Ù…ÛŒØ¯Ù† Ø§ÛŒÙ† Ù…ÙˆØ¶ÙˆØ¹ Ù…Ø«Ø§Ù„ Ø²ÛŒØ± Ø§Ø³Øª:
\begin{example}
\begin{equation*}
{}^{14}_{6}\text{C}
\qquad \text{versus} \qquad
{}^{14}_{\phantom{1}6}\text{C}
\end{equation*}
\end{example}
Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ ØªØ¹Ø¯Ø§Ø¯ Ø²ÛŒØ§Ø¯ÛŒ Ø§Ø² Ø§ÛŒØ²Ùˆâ€ŒØªÙˆÙ¾â€ŒÙ‡Ø§ Ø±Ø§ Ù‡Ù…Ø§Ù†Ù†Ø¯ Ù…Ø«Ø§Ù„ Ø¨Ø§Ù„Ø§ Ø¨Ù†ÙˆÛŒØ³ÛŒØ¯ØŒ Ø¨Ø³ØªÛ€  \pai{mhchem} Ø¨Ø±Ø§ÛŒ Ù†ÙˆØ´ØªÙ† ÙØ±Ù…ÙˆÙ„â€ŒÙ‡Ø§ÛŒ Ø´ÛŒÙ…ÛŒ Ø¨Ø³ÛŒØ§Ø± Ù…ÙÛŒØ¯ Ø§Ø³Øª.
\section{Ø±ÛŒØ²Ù‡â€ŒÚ©Ø§Ø±ÛŒ Ø¨Ø§ Ù‚Ù„Ù…â€ŒÙ‡Ø§ÛŒ Ø±ÛŒØ§Ø¶ÛŒ}\label{sec:fontsz}
Ù‚Ù„Ù…â€ŒÙ‡Ø§ÛŒ Ù…Ø®ØªÙ„Ù Ø±ÛŒØ§Ø¶ÛŒ Ø±Ø§ Ø¯Ø± Ø¬Ø¯ÙˆÙ„  
\ref{mathalpha}
%\LRE{\hyperref[mathalpha]{14.4}} 
Ø¯Ø± ØµÙØ­Ù‡ 
\pageref{mathalpha} Ø¢ÙˆØ±Ø¯Ù‡â€ŒØ§ÛŒÙ….
\begin{example}
 $\Re \qquad
  \mathcal{R} \qquad
  \mathfrak{R} \qquad
  \mathbb{R} \qquad $  
\end{example}
Ø¯ÙˆØªØ§ÛŒ Ø¢Ø®Ø± Ø¨Ù‡  \pai{amssymb} ÛŒØ§  \pai{amsfonts} Ø§Ø­ØªÛŒØ§Ø¬ Ø¯Ø§Ø±Ù†Ø¯.

Ú¯Ø§Ù‡ÛŒ Ø§ÙˆÙ‚Ø§Øª Ø¨Ø§ÛŒØ¯ Ø¨Ù‡ Ù„Ø§ØªÚ© Ø¨Ú¯ÙˆÛŒÛŒØ¯ Ú©Ù‡ Ø§Ù†Ø¯Ø§Ø²Ù‡ Ø±Ø§ ØªØµØ­ÛŒØ­ Ú©Ù†Ø¯. Ø¯Ø± Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒØŒ Ø§ÛŒÙ†â€ŒÚ©Ø§Ø± Ø±Ø§ Ø¨Ø§ ÙØ±Ù…Ø§Ù† Ø²ÛŒØ± Ø§Ù†Ø¬Ø§Ù… Ù…ÛŒâ€ŒØ¯Ù‡ÛŒÙ…:

\begin{latin}
\ci{displaystyle}~($\displaystyle 123$),
 \ci{textstyle}~($\textstyle 123$), 
\ci{scriptstyle}~($\scriptstyle 123$) \rl{Ùˆ}\\
\ci{scriptscriptstyle}~($\scriptscriptstyle 123$).
\end{latin}

Ø§Ú¯Ø± $\sum$ Ø¯Ø± ÛŒÚ© Ú©Ø³Ø± Ù‚Ø±Ø§Ø± Ø¯Ø§Ø´ØªÙ‡ Ø¨Ø§Ø´Ø¯ØŒ Ø¨Ù‡ Ø³Ø¨Ú© Ù…ØªÙ†ÛŒ Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†ÛŒ Ù…ÛŒâ€ŒØ´ÙˆØ¯ Ù…Ú¯Ø± Ø§ÛŒÙ† Ú©Ù‡ Ø¨Ù‡ Ù„Ø§ØªÚ© Ø§Ø·Ù„Ø§Ø¹ Ø¯Ù‡ÛŒØ¯:
\begin{example}
\begin{equation*}
 P = \frac{\displaystyle{ 
   \sum_{i=1}^n (x_i- x)
   (y_i- y)}} 
   {\displaystyle{\left[
   \sum_{i=1}^n(x_i-x)^2
   \sum_{i=1}^n(y_i- y)^2
   \right]^{1/2}}}
\end{equation*}    
\end{example}
ØªØºÛŒÛŒØ± Ø³Ø¨Ú© Ø¹Ù…ÙˆÙ…Ø§Ù‹ Ø±ÙˆÛŒ Ø¹Ù…Ù„Ú¯Ø±Ù‡Ø§ÛŒ Ø¨Ø²Ø±Ú¯ Ùˆ Ø­Ø¯ÙˆØ¯ Ø¢Ù†Ù‡Ø§ ØªØ§Ø«ÛŒØ± Ù…ÛŒâ€ŒÚ¯Ø°Ø§Ø±Ø¯.

% This is not a math accent, and no maths book would be set this way.
% mathop gets the spacing right.

\subsection{Ø­Ø±ÙˆÙ Ø³ÛŒØ§Ù‡}
\romanindex{bold symbols}\index{Ø­Ø±ÙˆÙ Ø³ÛŒØ§Ù‡}

Ù†ÙˆØ´ØªÙ† Ø­Ø±ÙˆÙ Ø³ÛŒØ§Ù‡ Ø¯Ø± Ù„Ø§ØªÚ© Ø³Ø®Øª Ø§Ø³ØªØ› ÛŒÚ© Ø­Ø±ÙˆÙâ€ŒÚ†ÛŒÙ†â€Œ Ø¢Ù…Ø§ØªÙˆØ± Ù…Ù…Ú©Ù† Ø§Ø³Øª Ø¨Ø®ÙˆØ§Ù‡Ø¯ Ø¨ÛŒØ´â€Œ Ø§Ø² â€ŒØ­Ø¯ Ø§Ø² Ø­Ø±ÙˆÙ Ø³ÛŒØ§Ù‡ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†Ø¯. ÙØ±Ù…Ø§Ù† ØªØºÛŒÛŒØ± Ù‚Ù„Ù… \verb|\mathbf| Ø­Ø±ÙˆÙ Ø³ÛŒØ§Ù‡ Ø±Ø§ ØªÙˆÙ„ÛŒØ¯ Ù…ÛŒâ€ŒÚ©Ù†Ø¯ØŒ Ø§Ù…Ø§ Ø§ÛŒÙ† Ø­Ø±ÙˆÙ Ø§ÛŒØ³ØªØ§Ø¯Ù‡ Ù‡Ø³ØªÙ†Ø¯ Ùˆ Ù†Ù…Ø§Ø¯Ù‡Ø§ÛŒ Ø±ÛŒØ§Ø¶ÛŒ Ø§ÛŒØªØ§Ù„ÛŒÚ© Ù‡Ø³ØªÙ†Ø¯ØŒ Ùˆ ÛŒÚ© ÙØ±Ù…Ø§Ù†  \ci{boldmath} ÙˆØ¬ÙˆØ¯ Ø¯Ø§Ø±Ø¯ØŒ \femph{Ø§ÛŒÙ† ÙØ±Ù…Ø§Ù† ØªÙ†Ù‡Ø§ Ø¨Ø§ÛŒØ¯ Ø¯Ø± Ø®Ø§Ø±Ø¬ Ø§Ø² Ø³Ø¨Ú© Ø±ÛŒØ§Ø¶ÛŒ Ù…ÙˆØ±Ø¯ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù‚Ø±Ø§Ø± Ú¯ÛŒØ±Ø¯}. 
Ø¨Ø§ Ø§ÛŒÙ† ÙˆØ¬ÙˆØ¯ Ø§Ø² Ø¢Ù† Ù…ÛŒâ€ŒØªÙˆØ§Ù† Ø¨Ø±Ø§ÛŒ Ù†Ù…Ø§Ø¯â€ŒÙ‡Ø§ Ù†ÛŒØ² Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ø±Ø¯:
\begin{example}
$\mu, M \qquad 
\mathbf{\mu}, \mathbf{M}$
\qquad \boldmath{$\mu, M$}
\end{example}

Ø¨Ø³ØªÛ€  \pai{amsbsy} (ØªÙˆØ³Ø· \pai{amsmath} ØªÙˆØ²ÛŒØ¹ Ù…ÛŒâ€ŒØ´ÙˆØ¯) 
Ùˆ Ù‡Ù…Ú†Ù†ÛŒÙ† 
\pai{bm} Ø§Ø² Ú©Ù„Ø§Ù \texttt{tools} Ø§ÛŒÙ†â€ŒÚ©Ø§Ø± Ø±Ø§ Ø¨Ø§ Ø§Ø±Ø§Ø¦Ù‡ ÙØ±Ù…Ø§Ù†  \ci{boldsymbol} Ø±Ø§Ø­Øªâ€ŒØªØ± Ù…ÛŒâ€ŒÚ©Ù†Ù†Ø¯:

\begin{example}
$\mu, M \qquad
\boldsymbol{\mu}, \boldsymbol{M}$
\end{example}
\section{Ù‚Ø¶ÛŒÙ‡â€ŒÙ‡Ø§ØŒ Ù‚Ø§Ù†ÙˆÙ†â€ŒÙ‡Ø§}

Ù‡Ù†Ú¯Ø§Ù… Ù†ÙˆØ´ØªÙ† Ù†ÙˆØ´ØªØ§Ø±â€Œâ€Œ Ø±ÛŒØ§Ø¶ÛŒØŒ Ù…Ù…Ú©Ù† Ø§Ø³Øª Ø¨Ù‡ Ù†ÙˆØ´ØªÙ† Ø³Ø§Ø®ØªØ§Ø±â€ŒÙ‡Ø§ÛŒÛŒ Ù…Ø§Ù†Ù†Ø¯ Ù‚Ø¶ÛŒÙ‡ØŒ ØªØ¹Ø±ÛŒÙØŒ Ø§ØµÙ„ØŒ Ùˆ ØºÛŒØ±Ù‡ Ø§Ø­ØªÛŒØ§Ø¬ Ù¾ÛŒØ¯Ø§ Ú©Ù†ÛŒØ¯.
\begin{lscommand}
\ci{newtheorem}\verb|{|\emph{name}\verb|}[|\emph{counter}\verb|]{|%
         \emph{text}\verb|}[|\emph{section}\verb|]|
\end{lscommand}
Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù† \emph{name} Ú©Ù„Ù…Ù‡ Ú©Ù„ÛŒØ¯ÛŒ Ø¨Ø±Ø§ÛŒ Ø´Ù†Ø§Ø³Ø§ÛŒÛŒ \lr{theorem} Ø§Ø³Øª. Ø¨Ø§ Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù† \emph{text} Ù†Ø§Ù… ÙˆØ§Ù‚Ø¹ÛŒ Ù‚Ø¶ÛŒÙ‡ Ø±Ø§ Ù…Ø¹Ø±ÙÛŒ Ù…ÛŒâ€ŒÚ©Ù†ÛŒØ¯ Ú©Ù‡ Ø¯Ø± Ø®Ø±ÙˆØ¬ÛŒ Ú†Ø§Ù¾ Ù…ÛŒâ€ŒØ´ÙˆØ¯.

Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù†â€ŒÙ‡Ø§ÛŒ Ø¯Ø±ÙˆÙ† Ú©Ø±ÙˆØ´Ù‡ Ø§Ø®ØªÛŒØ§Ø±ÛŒ Ù‡Ø³ØªÙ†Ø¯. Ø§Ø² Ø¢Ù†Ù‡Ø§ Ø¨Ø±Ø§ÛŒ Ù…Ø´Ø®Øµ Ú©Ø±Ø¯Ù† Ù†ÙˆØ¹ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ù‚Ø¶ÛŒÙ‡ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ø§Ø² Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù† \emph{counter} 
Ø¨Ø±Ø§ÛŒ Ù‡Ù…Ù†ÙˆØ¹ Ø´Ø¯Ù† Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ Ø¨Ø§ ÛŒÚ© Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ ØªØ¹Ø±ÛŒÙ Ø´Ø¯Ù‡ Ø§Ø³ØªÙØ§Ø¯Ù‡ Ù…ÛŒâ€ŒØ´ÙˆØ¯. Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù† \emph{section} Ø§Ø¬Ø§Ø²Ù‡ Ù…ÛŒâ€ŒØ¯Ù‡Ø¯ Ø¯Ø± Ø´Ù…Ø§Ø±Ù‡ Ù‚Ø¶ÛŒÙ‡ Ø´Ù…Ø§Ø±Ù‡ Ø¨Ø®Ø´ Ù†ÛŒØ² ÙˆØ§Ø±Ø¯ Ø´ÙˆØ¯.

Ø¨Ø¹Ø¯Ø§Ø² Ø§Ø¬Ø±Ø§ÛŒ ÙØ±Ù…Ø§Ù† \ci{newtheorem} Ø¯Ø± Ø³Ø±Ø¢ØºØ§Ø² Ù…Ø³ØªÙ†Ø¯ØªØ§Ù†ØŒ Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø§Ø² Ù…Ø­ÛŒØ· ØªØ¹Ø±ÛŒÙ Ø´Ø¯Ù‡ Ø¯Ø± Ù†ÙˆØ´ØªØ§Ø±â€Œ Ø¨Ù‡ Ø´Ú©Ù„ Ø²ÛŒØ± Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.
\begin{code}
\verb|\begin{|\emph{name}\verb|}[|\emph{text}\verb|]|\\
\lr{This is my interesting theorem}\\
\verb|\end{|\emph{name}\verb|}|     
\end{code}

Ø¨Ø³ØªÛ€ \pai{amsthm} (Ù‚Ø³Ù…ØªÛŒ Ø§Ø² \lr{\AmS-\LaTeX}) 
ÙØ±Ù…Ø§Ù† \verb|}|\emph{style}\verb|{|\ci{theoremstyle}
Ø±Ø§ Ø§Ø±Ø§Ø¦Ù‡ Ù…ÛŒâ€ŒÚ©Ù†Ø¯ Ú©Ù‡ ØªÙˆØ³Ø· Ø¢Ù† Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø§Ø² Ù…Ø­ÛŒØ·â€ŒÙ‡Ø§ÛŒ Ø§Ø² Ù¾ÛŒØ´â€ŒØªØ¹Ø±ÛŒÙâ€ŒØ´Ø¯Ù‡  Ù…Ø§Ù†Ù†Ø¯ \texttt{definition} (ØªÛŒØªØ± Ø¨Ø²Ø±Ú¯ØŒ Ø¨Ø¯Ù†Ù‡ Ø±ÙˆÙ…Ù†)ØŒ
\texttt{plain} (ØªÛŒØªØ± Ø¨Ø²Ø±Ú¯ØŒ Ø¨Ø¯Ù†Ù‡ Ø§ÛŒØªØ§Ù„ÛŒÚ©) 
ÛŒØ§ \texttt{remark} (ØªÛŒØªØ± Ø§ÛŒØªØ§Ù„ÛŒÚ©ØŒ Ø¨Ø¯Ù†Ù‡ Ø±ÙˆÙ…Ù†) 
Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.

ØªØ¦ÙˆØ±ÛŒ Ø¨Ø³ Ø§Ø³Øª. Ù…Ø«Ø§Ù„â€ŒÙ‡Ø§ÛŒ Ø²ÛŒØ± Ù‡Ø± Ù†ÙˆØ¹ Ø§Ø¨Ù‡Ø§Ù…ÛŒ Ø±Ø§ Ø§Ø² Ø¨ÛŒÙ† Ù…ÛŒâ€ŒØ¨Ø±Ø¯ Ùˆ Ù…Ø´Ø®Øµ Ù…ÛŒâ€ŒÚ©Ù†Ø¯ Ù…Ø­ÛŒØ· 
\verb|\newtheorem| Ú©Ù…ÛŒ Ø¨Ø±Ø§ÛŒ ÙÙ‡Ù…ÛŒØ¯Ù† Ù…Ø´Ú©Ù„ Ø§Ø³Øª.

% actually define things
\begin{latin}
\theoremstyle{definition} \newtheorem{law}{Law}
\theoremstyle{plain}      \newtheorem{jury}[law]{Jury}
\theoremstyle{remark}     \newtheorem*{marg}{Margaret}
\end{latin}

Ø§Ø¨ØªØ¯Ø§ Ù‚Ø¶ÛŒÙ‡â€ŒÙ‡Ø§ Ø±Ø§ ØªØ¹Ø±ÛŒÙ Ù…ÛŒâ€ŒÚ©Ù†ÛŒÙ…:
\begin{latin}
\begin{verbatim}
\theoremstyle{definition} \newtheorem{law}{Law}
\theoremstyle{plain}      \newtheorem{jury}[law]{Jury}
\theoremstyle{remark}     \newtheorem*{marg}{Margaret}
\end{verbatim}
\end{latin}


\begin{example}
\begin{law} \label{law:box}
Don't hide in the witness box
\end{law}
\begin{jury}[The Twelve]
It could be you! So beware and
see law~\ref{law:box}.\end{jury}
\begin{marg}No, No, No\end{marg}
\end{example}


Ù‚Ø¶ÛŒÙ‡Ù” \lr{Jury} Ø¯Ø§Ø±Ø§ÛŒ Ø´Ù…Ø§Ø±Ù‡â€ŒÚ¯Ø°Ø§Ø±ÛŒ \lr{Law} Ø§Ø³ØªØŒ Ø¨Ù†Ø§Ø¨Ø±Ø§ÛŒÙ† Ø´Ù…Ø§Ø±Ù‡â€ŒØ§ÛŒ Ø±Ø§ Ø§Ø®Ø° Ù…ÛŒâ€ŒÚ©Ù†Ø¯ Ú©Ù‡ Ø¯Ø± Ø¯Ù†Ø¨Ø§Ù„Ù‡Ù” Ø´Ù…Ø§Ø±Ù‡Ù” \lr{Laws} Ø§Ø³Øª.  Ø¢Ø±Ú¯ÙˆÙ…Ø§Ù† Ø¯Ø§Ø®Ù„ Ú©Ø±ÙˆØ´Ù‡ Ø¨Ø±Ø§ÛŒ Ù…Ø¹ÛŒÙ† Ú©Ø±Ø¯Ù† ÛŒÚ© Ø¹Ù†ÙˆØ§Ù† Ø´Ø¨ÛŒÙ‡ Ù‚Ø¶ÛŒÙ‡ Ø§Ø³Øª.


\begin{example}
\newtheorem{mur}{Murphy}[section]


\begin{mur} If there are two or 
more ways to do something, and 
one of those ways can result in
a catastrophe, then someone 
will do it.\end{mur}
\end{example}



Ù‚Ø¶ÛŒÙ‡Ù” \lr{Murphy} Ø´Ù…Ø§Ø±Ù‡â€ŒØ§ÛŒ ÙˆØ§Ø¨Ø³ØªÙ‡ Ø¨Ù‡ Ø´Ù…Ø§Ø±Ù‡Ù” Ø¨Ø®Ø´ Ø¬Ø§Ø±ÛŒ Ø§Ø®Ø° Ù…ÛŒâ€ŒÚ©Ù†Ø¯. Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø¨Ù‡â€ŒØ¬Ø§ÛŒ Ø¨Ø®Ø´ Ø§Ø² ÙØµÙ„ Ùˆ Ø´Ø¨ÛŒÙ‡ Ø¢Ù† Ø§Ø³ØªÙØ§Ø¯Ù‡ Ú©Ù†ÛŒØ¯.

Ø¨Ø³ØªÛ€ \pai{amsthm} Ø¯Ø§Ø±Ø§ÛŒ Ù…Ø­ÛŒØ· \ei{proof} Ù†ÛŒØ² Ø§Ø³Øª.

\renewcommand\proofname{Proof}
\begin{example}
\begin{proof}
 Trivial, use
\[E=mc^2\]
\end{proof}
\end{example}


Ø¨Ø§ ÙØ±Ù…Ø§Ù† \ci{qedhere} Ù…ÛŒâ€ŒØªÙˆØ§Ù†ÛŒØ¯ Ø¹Ù„Ø§Ù…Øª Ø§Ù†ØªÙ‡Ø§ÛŒ Ø§Ø«Ø¨Ø§Øª Ø±Ø§ Ø¯Ø± Ù…ÙˆØ§Ù‚Ø¹ÛŒ Ú©Ù‡ Ø¨Ù‡â€ŒØªÙ†Ù‡Ø§ÛŒÛŒ Ø¯Ø± ÛŒÚ© Ø®Ø· Ù‚Ø±Ø§Ø± Ø¯Ø§Ø±Ø¯ Ø¯Ø± Ù…Ú©Ø§Ù† Ù…Ù†Ø§Ø³Ø¨ÛŒ Ø¯Ø±Ø¬ Ú©Ù†ÛŒØ¯.

\begin{example}
\begin{proof}
 Trivial, use
\[E=mc^2 \qedhere\]
\end{proof}
\end{example}

Ø§Ú¯Ø± Ù…ÛŒâ€ŒØ®ÙˆØ§Ù‡ÛŒØ¯ ØªØ§ Ù…Ø­ÛŒØ· Ù…Ù†Ø§Ø³Ø¨ÛŒ Ø¨Ø±Ø§ÛŒ Ø®ÙˆØ¯ Ø·Ø±Ø§Ø­ÛŒ Ú©Ù†ÛŒØ¯ØŒ Ø¨Ø³ØªÛ€ \pai{ntheorem} Ú¯Ø²ÛŒÙ†Ù‡â€ŒÙ‡Ø§ÛŒ Ø¨Ø³ÛŒØ§Ø± Ø²ÛŒØ§Ø¯ÛŒ Ø¯Ø± Ø§Ø®ØªÛŒØ§Ø±ØªØ§Ù† Ù‚Ø±Ø§Ø± Ù…ÛŒâ€ŒØ¯Ù‡Ø¯.



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