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authorKarl Berry <karl@freefriends.org>2007-10-04 13:18:10 +0000
committerKarl Berry <karl@freefriends.org>2007-10-04 13:18:10 +0000
commit5826df3d62bb59d12a4eae90e2c62379defeae05 (patch)
tree9c69d3c78f89f543f300d6bddcd98af61294d2f5 /Master/texmf-dist/doc/latex/ijmart
parent093bb11a0c1a93d269217ee705cff6ecf08faf0e (diff)
ijmart 1.1 (3oct07)
git-svn-id: svn://tug.org/texlive/trunk@5109 c570f23f-e606-0410-a88d-b1316a301751
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@@ -1137,6 +1137,38 @@ which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$
\cite{mami:matrixth}.
\end{thm}
+\section{Named Propositions}
+\label{s:namedprops}
+
+Here we discuss several propositions:
+\begin{namedprop}{plain}{thm}{G\"odel Theorem}[First incompleteness theorem]
+ For any consistent formal, computably enumerable theory that proves
+ basic arithmetical truths, an arithmetical statement that is true,
+ but not provable in the theory, can be constructed. That is, any
+ effectively generated theory capable of expressing elementary
+ arithmetic cannot be both consistent and complete.
+\end{namedprop}
+
+\begin{namedprop}{plain}{thm}{G\"odel Theorem}
+ For any formal recursively enumerable (i.e. effectively generated)
+ theory T including basic arithmetical truths and also certain truths
+ about formal provability, T includes a statement of its own
+ consistency if and only if T is inconsistent.
+\end{namedprop}
+
+\begin{namedprop*}{plain}{Abel's Lemma}[Summation by parts]
+ For any sequences $f_k$ and $g_k$
+ \begin{displaymath}
+ \sum_{k=m}^n f_k(g_{k+1}-g_k) = f_{n+1}g_{n+1} -
+ \sum_{k=m}^n g_{k+1} (f_{k+1} - f_k)
+ \end{displaymath}
+\end{namedprop*}
+
+\begin{namedprop*}{plain}{Fermat's last theorem}
+ For any $n>2$ the equation $x^n+y^n=z^n$ has no non-zero integer
+ solutions.
+\end{namedprop*}
+
\section{Various font features of the \pkg{amsmath} package}
\label{s:font}
\subsection{Bold versions of special symbols}