From 5826df3d62bb59d12a4eae90e2c62379defeae05 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Thu, 4 Oct 2007 13:18:10 +0000 Subject: ijmart 1.1 (3oct07) git-svn-id: svn://tug.org/texlive/trunk@5109 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/ijmart/ijmart.pdf | Bin 275853 -> 290552 bytes Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf | Bin 387985 -> 390694 bytes Master/texmf-dist/doc/latex/ijmart/ijmsample.tex | 32 +++++++++++++++++++++++ 3 files changed, 32 insertions(+) (limited to 'Master/texmf-dist/doc/latex/ijmart') diff --git a/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf b/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf index 456be1bb11e..9407fea61d7 100644 Binary files a/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf and b/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf differ diff --git a/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf b/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf index 7c346f4996b..239b34671bb 100644 Binary files a/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf and b/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf differ diff --git a/Master/texmf-dist/doc/latex/ijmart/ijmsample.tex b/Master/texmf-dist/doc/latex/ijmart/ijmsample.tex index 7c44ef9c8dc..ba9809a6901 100644 --- a/Master/texmf-dist/doc/latex/ijmart/ijmsample.tex +++ b/Master/texmf-dist/doc/latex/ijmart/ijmsample.tex @@ -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} -- cgit v1.2.3