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diff --git a/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf b/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf Binary files differindex 456be1bb11e..9407fea61d7 100644 --- a/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf +++ b/Master/texmf-dist/doc/latex/ijmart/ijmart.pdf diff --git a/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf b/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf Binary files differindex 7c346f4996b..239b34671bb 100644 --- a/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf +++ b/Master/texmf-dist/doc/latex/ijmart/ijmsample.pdf 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} |