trunk/c_glo1/c_glo1.tex

%$Header$

\chapter*{Glossary Of Mathematical And Other Notation}
\markboth{GLOSSARY OF MATHEMATICAL NOTATION}{GLOSSARY OF MATHEMATICAL NOTATION}

\label{cglo1}

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\section*{General Notation}

\begin{vworkmathtermglossaryenum}

\item \mbox{\boldmath $ \vworkdivides $}


      $a \vworkdivides b$, 
      \index{divides@divides ($\vworkdivides$)}
      \index{--@$\vworkdivides$ (divides)}
      read ``\emph{$a$ divides $b$}'', denotes that $b/a$ has no remainder.
      Equivalently, it may be stated that
      $(a \vworkdivides b) \Rightarrow (\exists c \in \vworkintset{}, b = ac)$.

\item \mbox{\boldmath $ \vworknotdivides $}

      $a \vworknotdivides b$, 
      \index{divides@divides ($\vworkdivides$)}
      \index{--@$\vworknotdivides$ (doesn't divide)}
      read ``\emph{$a$ does not divide $b$}'', denotes that $b/a$ has a reminder.
      Equivalently, it may be stated that
      $(a \vworknotdivides b) \Rightarrow (\nexists c \in \vworkintset{}, b = ac)$.

\item \mbox{\boldmath $ \lfloor \cdot \rfloor $}

      Used
      \index{floor function@floor function ($\lfloor\cdot\rfloor$)}
      \index{--@$\lfloor\cdot\rfloor$ (\emph{floor($\cdot$)} function)}
      to denote the \emph{floor($\cdot$)} function.  The
      \emph{floor($\cdot$)}
      function is the largest integer not larger than the
      argument.

\item \mbox{\boldmath $\lceil \cdot \rceil$ }

      Used
      \index{ceiling function@ceiling function ($\lceil\cdot\rceil$)}
      \index{--@$\lceil\cdot\rceil$ (\emph{ceiling($\cdot$)} function)}
      to denote the \emph{ceiling($\cdot$)} function.
      The \emph{ceiling($\cdot$)} function
      is the smallest integer not smaller than the
      argument.
\end{vworkmathtermglossaryenum}

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\section*{Usage Of English And Greek Letters}

\begin{vworkmathtermglossaryenum}

\item \mbox {\boldmath $a/b$}

      An arbitrary \index{rational number}rational number.

\item \mbox {\boldmath $ F_N $}

      The \index{Farey series}Farey 
      series of order $N$.  The Farey series is the
      ordered set of irreducible rational numbers 
          in [0,1] with a
      denominator not larger than $N$.

\item \mbox {\boldmath $F_{k_{MAX}, \overline{h_{MAX}}}$}
      
          \index{FKMAXHMAX@$F_{k_{MAX}, \overline{h_{MAX}}}$}
          The ordered set of irreducible rational numbers
          $h/k$ subject to the constraints $0 \leq h \leq h_{MAX}$
          and $1 \leq k \leq h_{MAX}$.  
          (See Section \cfryzeroxrefhyphen{}\ref{cfry0:schk0}.)


\item \mbox{\boldmath $H/K$}, \mbox{\boldmath $h/k$},
      \mbox{\boldmath $h'/k'$}, \mbox{\boldmath $h''/k''$},
      \mbox{\boldmath $h_i/k_i$}

      Terms in a Farey series of order $N$.

\item \mbox{\boldmath $r_A$}

      The rational number $h/k$ used to approximate
      an arbitrary real number $r_I$.

\item \mbox{\boldmath $r_I$}

      The real number, which may or may not be rational,
      which is to be approximated by a rational number
      $r_A = h/k$.

\item \textbf{reduced}

      See \emph{irreducible}.

\item \mbox{\boldmath $s_k = p_k/q_k$}

      The $k$th convergent of a continued fraction.

\item \mbox{\boldmath $x_{MAX}$}

      The largest element of the domain for which the
      behavior of an approximation must be guaranteed.
      In this paper, most derivations assume
      that $x \in [0, x_{MAX}]$, $x_{MAX} \in \vworkintsetpos{}$.
\end{vworkmathtermglossaryenum}

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\section*{Bitfields And Portions Of Integers}

\begin{vworkmathtermglossaryenum}
\item \mbox{\boldmath $a_{b}$}

      The $b$th bit of the integer $a$.  Bits are numbered with the
      least significant bit ``0'', and consecutively through 
      ``$n-1$'', where $n$ is the total number of bits.

      In general, if $p$ is an $n$-bit unsigned integer,

      \begin{equation}
      \nonumber p = \sum_{i=0}^{n-1} 2^i p_i .
      \end{equation}

\item \mbox{\boldmath $a_{c:b}$}

      The integer consisting of the $b$th through the
      $c$th bits of the integer $a$.  Bits are numbered with the
      least significant bit ``0'', and consecutively through 
      ``$n-1$'', where $n$ is the total number of bits.

      For example, if $p$ is a 24-bit unsigned integer, then

      \begin{equation}
      \nonumber p = 2^{16}p_{23:16} + 2^{8}p_{15:8} + p_{7:0} .
      \end{equation}

\item \mbox{\boldmath $a_{[b]}$}

      The $b$th word of the integer $a$.  Words are numbered 
      with the
      least significant word ``0'', and consecutively through 
      ``$n-1$'', where $n$ is the total number of words.

      In general, if $p$ is an $n$-word unsigned integer 
      and $z$ is the wordsize in bits,

      \begin{equation}
      \nonumber p = \sum_{i=0}^{n-1} 2^{iz} p_i .
      \end{equation}

\item \mbox{\boldmath $a_{[c:b]}$}

      The integer consisting of the $b$th through the
      $c$th word of the integer $a$.  Words are numbered with the
      least significant word ``0'', and consecutively through 
      ``$n-1$'', where $n$ is the total number of words.

      For example, if $p$ is a 24-word unsigned integer and
      $z$ is the wordsize in bits, then

      \begin{equation}
      \nonumber p = 2^{16z}p_{[23:16]} + 2^{8z}p_{[15:8]} + p_{[7:0]} .
      \end{equation}

\end{vworkmathtermglossaryenum}

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\section*{Matrices And Vectors}

\begin{vworkmathtermglossaryenum}

\item \mbox{\boldmath $0$}

      $\mathbf{0}$ (in bold face) is used to denote either a vector or matrix
      populated with all zeroes.  Optionally, in cases where the context is not clear
      or where there is cause to highlight the dimension, $\mathbf{0}$ may be subscripted
      to indicate the dimension, i.e. 
      
      \begin{equation}
      \nonumber
      \mathbf{0}_3 = \left[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right]
      \end{equation}

      \begin{equation}
      \nonumber
      \mathbf{0}_{3 \times 2} = \left[\begin{array}{cc} 0&0 \\ 0&0 \\ 0&0 \end{array}\right]
      \end{equation}

\item \mbox{\boldmath $I$}

      $I$ is used to denote the square identity matrix (the matrix with all
      elements 0 except elements on the diagonal which are 1).
      Optionally, in cases where the context is not clear
      or where there is cause to highlight the dimension, $I$ may be subscripted
      to indicate the dimension, i.e. 
      
      \begin{equation}
      \nonumber
      I = I_3 = I_{3 \times 3} = \left[\begin{array}{ccc} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}\right]
      \end{equation}

\end{vworkmathtermglossaryenum}


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\section*{Sets And Set Notation}

\begin{vworkmathtermglossaryenum}

\item \mbox{\boldmath $n(A)$}

      The \index{cardinality}cardinality of set $A$.  (The cardinality of a set is the
      number of elements in the set.)

\end{vworkmathtermglossaryenum}

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\section*{Sets Of Numbers}

\begin{vworkmathtermglossaryenum}

\item \mbox{\boldmath $\vworkintsetpos$}

      The 
      \index{natural number}
      \index{N@$\vworkintsetpos$}
      set of positive integers (natural numbers).

\item \mbox{\boldmath $\vworkratset$}

      The 
      \index{rational number}
      \index{Q@$\vworkratset$}
      set of rational numbers.

\item \mbox{\boldmath $\vworkratsetnonneg$}

      The 
      \index{rational number}
      \index{Q+@$\vworkratsetnonneg$}
      set of non-negative rational numbers.

\item \mbox{\boldmath $\vworkrealset$}

      The 
      \index{real number}
      \index{R@$\vworkrealset$}
      set of real numbers.

\item \mbox{\boldmath $\vworkrealsetnonneg$}

      The 
      \index{real number}
      \index{R+@$\vworkrealsetnonneg$}
      set of non-negative real numbers.

\item \mbox{\boldmath $\vworkintset$}

      The 
      \index{integer}
      \index{Z@$\vworkintset$}
      set of integers.

\item \mbox{\boldmath $\vworkintsetnonneg$}

      The 
      \index{integer}
      \index{Z+@$\vworkintsetnonneg$}
      set of non-negative integers.

\end{vworkmathtermglossaryenum}


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\noindent\begin{figure}[!b]
\noindent\rule[-0.25in]{\textwidth}{1pt}
\begin{tiny}
\begin{verbatim}
$RCSfile: c_glo1.tex,v $
$Source: /home/dashley/cvsrep/e3ft_gpl01/e3ft_gpl01/dtaipubs/esrgubka/c_glo1/c_glo1.tex,v $
$Revision: 1.7 $
$Author: dtashley $
$Date: 2003/03/13 06:28:13 $
\end{verbatim}
\end{tiny}
\noindent\rule[0.25in]{\textwidth}{1pt}
\end{figure}

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% $Log: c_glo1.tex,v $
% Revision 1.7  2003/03/13 06:28:13  dtashley
% Cardinality definition and notation added.
%
% Revision 1.6  2002/11/22 02:21:38  dtashley
% Substantial edits.
%
% Revision 1.5  2002/07/29 16:30:09  dtashley
% Safety checkin before moving work back to WSU server Kalman.
%
% Revision 1.4  2001/08/16 19:53:27  dtashley
% Beginning to prepare for v1.05 release.
%
% Revision 1.3  2001/07/01 19:10:30  dtashley
% LOG keyword expansion problem corrected.
%
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% $History: c_glo1.tex $
% 
% *****************  Version 3  *****************
% User: Dashley1     Date: 1/31/01    Time: 4:20p
% Updated in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
% Edits.
% 
% *****************  Version 2  *****************
% User: Dashley1     Date: 8/08/00    Time: 10:53a
% Updated in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
% Correction of DIVIDES and NOT DIVIDES symbols.
%
% *****************  Version 1  *****************
% User: David T. Ashley Date: 7/30/00    Time: 6:48p
% Created in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
% Initial check-in.
%
%End of file C_GLO1.TEX
1	%$Header$
2
3	\chapter*{Glossary Of Mathematical And Other Notation}
4	\markboth{GLOSSARY OF MATHEMATICAL NOTATION}{GLOSSARY OF MATHEMATICAL NOTATION}
5
6	\label{cglo1}
7
8	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
9	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
11
12	\section*{General Notation}
13
14	\begin{vworkmathtermglossaryenum}
15
16	\item \mbox{\boldmath $ \vworkdivides $}
17
18
19	$a \vworkdivides b$,
20	\index{divides@divides ($\vworkdivides$)}
21	\index{--@$\vworkdivides$ (divides)}
22	read ``\emph{$a$ divides $b$}'', denotes that $b/a$ has no remainder.
23	Equivalently, it may be stated that
24	$(a \vworkdivides b) \Rightarrow (\exists c \in \vworkintset{}, b = ac)$.
25
26	\item \mbox{\boldmath $ \vworknotdivides $}
27
28	$a \vworknotdivides b$,
29	\index{divides@divides ($\vworkdivides$)}
30	\index{--@$\vworknotdivides$ (doesn't divide)}
31	read ``\emph{$a$ does not divide $b$}'', denotes that $b/a$ has a reminder.
32	Equivalently, it may be stated that
33	$(a \vworknotdivides b) \Rightarrow (\nexists c \in \vworkintset{}, b = ac)$.
34
35	\item \mbox{\boldmath $ \lfloor \cdot \rfloor $}
36
37	Used
38	\index{floor function@floor function ($\lfloor\cdot\rfloor$)}
39	\index{--@$\lfloor\cdot\rfloor$ (\emph{floor($\cdot$)} function)}
40	to denote the \emph{floor($\cdot$)} function. The
41	\emph{floor($\cdot$)}
42	function is the largest integer not larger than the
43	argument.
44
45	\item \mbox{\boldmath $\lceil \cdot \rceil$ }
46
47	Used
48	\index{ceiling function@ceiling function ($\lceil\cdot\rceil$)}
49	\index{--@$\lceil\cdot\rceil$ (\emph{ceiling($\cdot$)} function)}
50	to denote the \emph{ceiling($\cdot$)} function.
51	The \emph{ceiling($\cdot$)} function
52	is the smallest integer not smaller than the
53	argument.
54	\end{vworkmathtermglossaryenum}
55
56	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
57	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
58	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
59
60	\section*{Usage Of English And Greek Letters}
61
62	\begin{vworkmathtermglossaryenum}
63
64	\item \mbox {\boldmath $a/b$}
65
66	An arbitrary \index{rational number}rational number.
67
68	\item \mbox {\boldmath $ F_N $}
69
70	The \index{Farey series}Farey
71	series of order $N$. The Farey series is the
72	ordered set of irreducible rational numbers
73	in [0,1] with a
74	denominator not larger than $N$.
75
76	\item \mbox {\boldmath $F_{k_{MAX}, \overline{h_{MAX}}}$}
77
78	\index{FKMAXHMAX@$F_{k_{MAX}, \overline{h_{MAX}}}$}
79	The ordered set of irreducible rational numbers
80	$h/k$ subject to the constraints $0 \leq h \leq h_{MAX}$
81	and $1 \leq k \leq h_{MAX}$.
82	(See Section \cfryzeroxrefhyphen{}\ref{cfry0:schk0}.)
83
84
85	\item \mbox{\boldmath $H/K$}, \mbox{\boldmath $h/k$},
86	\mbox{\boldmath $h'/k'$}, \mbox{\boldmath $h''/k''$},
87	\mbox{\boldmath $h_i/k_i$}
88
89	Terms in a Farey series of order $N$.
90
91	\item \mbox{\boldmath $r_A$}
92
93	The rational number $h/k$ used to approximate
94	an arbitrary real number $r_I$.
95
96	\item \mbox{\boldmath $r_I$}
97
98	The real number, which may or may not be rational,
99	which is to be approximated by a rational number
100	$r_A = h/k$.
101
102	\item \textbf{reduced}
103
104	See \emph{irreducible}.
105
106	\item \mbox{\boldmath $s_k = p_k/q_k$}
107
108	The $k$th convergent of a continued fraction.
109
110	\item \mbox{\boldmath $x_{MAX}$}
111
112	The largest element of the domain for which the
113	behavior of an approximation must be guaranteed.
114	In this paper, most derivations assume
115	that $x \in [0, x_{MAX}]$, $x_{MAX} \in \vworkintsetpos{}$.
116	\end{vworkmathtermglossaryenum}
117
118	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
119	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
120	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
121
122	\section*{Bitfields And Portions Of Integers}
123
124	\begin{vworkmathtermglossaryenum}
125	\item \mbox{\boldmath $a_{b}$}
126
127	The $b$th bit of the integer $a$. Bits are numbered with the
128	least significant bit ``0'', and consecutively through
129	``$n-1$'', where $n$ is the total number of bits.
130
131	In general, if $p$ is an $n$-bit unsigned integer,
132
133	\begin{equation}
134	\nonumber p = \sum_{i=0}^{n-1} 2^i p_i .
135	\end{equation}
136
137	\item \mbox{\boldmath $a_{c:b}$}
138
139	The integer consisting of the $b$th through the
140	$c$th bits of the integer $a$. Bits are numbered with the
141	least significant bit ``0'', and consecutively through
142	``$n-1$'', where $n$ is the total number of bits.
143
144	For example, if $p$ is a 24-bit unsigned integer, then
145
146	\begin{equation}
147	\nonumber p = 2^{16}p_{23:16} + 2^{8}p_{15:8} + p_{7:0} .
148	\end{equation}
149
150	\item \mbox{\boldmath $a_{[b]}$}
151
152	The $b$th word of the integer $a$. Words are numbered
153	with the
154	least significant word ``0'', and consecutively through
155	``$n-1$'', where $n$ is the total number of words.
156
157	In general, if $p$ is an $n$-word unsigned integer
158	and $z$ is the wordsize in bits,
159
160	\begin{equation}
161	\nonumber p = \sum_{i=0}^{n-1} 2^{iz} p_i .
162	\end{equation}
163
164	\item \mbox{\boldmath $a_{[c:b]}$}
165
166	The integer consisting of the $b$th through the
167	$c$th word of the integer $a$. Words are numbered with the
168	least significant word ``0'', and consecutively through
169	``$n-1$'', where $n$ is the total number of words.
170
171	For example, if $p$ is a 24-word unsigned integer and
172	$z$ is the wordsize in bits, then
173
174	\begin{equation}
175	\nonumber p = 2^{16z}p_{[23:16]} + 2^{8z}p_{[15:8]} + p_{[7:0]} .
176	\end{equation}
177
178	\end{vworkmathtermglossaryenum}
179
180	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
181	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
182	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
183
184	\section*{Matrices And Vectors}
185
186	\begin{vworkmathtermglossaryenum}
187
188	\item \mbox{\boldmath $0$}
189
190	$\mathbf{0}$ (in bold face) is used to denote either a vector or matrix
191	populated with all zeroes. Optionally, in cases where the context is not clear
192	or where there is cause to highlight the dimension, $\mathbf{0}$ may be subscripted
193	to indicate the dimension, i.e.
194
195	\begin{equation}
196	\nonumber
197	\mathbf{0}_3 = \left[\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right]
198	\end{equation}
199
200	\begin{equation}
201	\nonumber
202	\mathbf{0}_{3 \times 2} = \left[\begin{array}{cc} 0&0 \\ 0&0 \\ 0&0 \end{array}\right]
203	\end{equation}
204
205	\item \mbox{\boldmath $I$}
206
207	$I$ is used to denote the square identity matrix (the matrix with all
208	elements 0 except elements on the diagonal which are 1).
209	Optionally, in cases where the context is not clear
210	or where there is cause to highlight the dimension, $I$ may be subscripted
211	to indicate the dimension, i.e.
212
213	\begin{equation}
214	\nonumber
215	I = I_3 = I_{3 \times 3} = \left[\begin{array}{ccc} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}\right]
216	\end{equation}
217
218	\end{vworkmathtermglossaryenum}
219
220
221	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
222	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
223	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
224
225	\section*{Sets And Set Notation}
226
227	\begin{vworkmathtermglossaryenum}
228
229	\item \mbox{\boldmath $n(A)$}
230
231	The \index{cardinality}cardinality of set $A$. (The cardinality of a set is the
232	number of elements in the set.)
233
234	\end{vworkmathtermglossaryenum}
235
236	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
237	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
238	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
239
240	\section*{Sets Of Numbers}
241
242	\begin{vworkmathtermglossaryenum}
243
244	\item \mbox{\boldmath $\vworkintsetpos$}
245
246	The
247	\index{natural number}
248	\index{N@$\vworkintsetpos$}
249	set of positive integers (natural numbers).
250
251	\item \mbox{\boldmath $\vworkratset$}
252
253	The
254	\index{rational number}
255	\index{Q@$\vworkratset$}
256	set of rational numbers.
257
258	\item \mbox{\boldmath $\vworkratsetnonneg$}
259
260	The
261	\index{rational number}
262	\index{Q+@$\vworkratsetnonneg$}
263	set of non-negative rational numbers.
264
265	\item \mbox{\boldmath $\vworkrealset$}
266
267	The
268	\index{real number}
269	\index{R@$\vworkrealset$}
270	set of real numbers.
271
272	\item \mbox{\boldmath $\vworkrealsetnonneg$}
273
274	The
275	\index{real number}
276	\index{R+@$\vworkrealsetnonneg$}
277	set of non-negative real numbers.
278
279	\item \mbox{\boldmath $\vworkintset$}
280
281	The
282	\index{integer}
283	\index{Z@$\vworkintset$}
284	set of integers.
285
286	\item \mbox{\boldmath $\vworkintsetnonneg$}
287
288	The
289	\index{integer}
290	\index{Z+@$\vworkintsetnonneg$}
291	set of non-negative integers.
292
293	\end{vworkmathtermglossaryenum}
294
295
296	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
297	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
298	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
299
300	\noindent\begin{figure}[!b]
301	\noindent\rule[-0.25in]{\textwidth}{1pt}
302	\begin{tiny}
303	\begin{verbatim}
304	$RCSfile: c_glo1.tex,v $
305	$Source: /home/dashley/cvsrep/e3ft_gpl01/e3ft_gpl01/dtaipubs/esrgubka/c_glo1/c_glo1.tex,v $
306	$Revision: 1.7 $
307	$Author: dtashley $
308	$Date: 2003/03/13 06:28:13 $
309	\end{verbatim}
310	\end{tiny}
311	\noindent\rule[0.25in]{\textwidth}{1pt}
312	\end{figure}
313
314	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
315	% $Log: c_glo1.tex,v $
316	% Revision 1.7 2003/03/13 06:28:13 dtashley
317	% Cardinality definition and notation added.
318	%
319	% Revision 1.6 2002/11/22 02:21:38 dtashley
320	% Substantial edits.
321	%
322	% Revision 1.5 2002/07/29 16:30:09 dtashley
323	% Safety checkin before moving work back to WSU server Kalman.
324	%
325	% Revision 1.4 2001/08/16 19:53:27 dtashley
326	% Beginning to prepare for v1.05 release.
327	%
328	% Revision 1.3 2001/07/01 19:10:30 dtashley
329	% LOG keyword expansion problem corrected.
330	%
331	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
332	% $History: c_glo1.tex $
333	%
334	% *************** Version 3 ***************
335	% User: Dashley1 Date: 1/31/01 Time: 4:20p
336	% Updated in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
337	% Edits.
338	%
339	% *************** Version 2 ***************
340	% User: Dashley1 Date: 8/08/00 Time: 10:53a
341	% Updated in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
342	% Correction of DIVIDES and NOT DIVIDES symbols.
343	%
344	% *************** Version 1 ***************
345	% User: David T. Ashley Date: 7/30/00 Time: 6:48p
346	% Created in $/uC Software Multi-Volume Book (A)/Chapter, GLO1, Glossary Of Mathematical Notation
347	% Initial check-in.
348	%
349	%End of file C_GLO1.TEX