Minimal Working Example
\documentclass[12pt,letterpaper]{article}
\newtheorem{theorem}{Theorem}
\begin{document}
\section{Introduction}
Theorems can easily be defined:
\begin{theorem}
A definition is an exact and concise explanation of a single concept or word.
\end{theorem}
\end{document}
Numbered Theorems, Definitions, Corollaries and Lemmas
Numbered environments in LaTeX can be defined by means of the command \newtheorem :
\newtheorem{environment name}{Text}[parent counter]
\newtheorem{environment name}[shared counter]{Text}
- Put command in the preamble.
- The name/label {environment name} of the environment that is defined.
- The name {environment name} you will use to reference inside a theorem-like environment \begin{environment name}[environment caption]
\end{environment name}. - The word {Text/Printed Output} that will be printed, in boldface font, at the beginning of the environment.
- The additional argument / optional argument [parent counter/sequential level/numberby/hierarchy name/outer counter] is the name of the sequential level (often by section/subsection/etc.) at which the numbering is to take place / the environment counter is reset every time parent counter is incremented.
- The additional argument / optional argument [shared counter/sequential level/numberby/hierarchy name/inner counter] is the name of the sequential level at which the numbering is to take place / the environment counter is reset every time shared counter is incremented.
The statement of any theorem can then be enclosed between \begin{theorem} and \end{theorem}:
\begin{environment name}[environment caption]
\end{environment name}
- Put command into the body of your document.
- You can put a environment caption / theorem’s traditional name, date, discoverer/scientist, or the similar in square brackets. The environment caption prints at the beginning of the paragraph and inside Parentheses / round bracket.
- The theorem will be labelled/titled and numbered by LaTeX, and the statement of the theorem with be automatically italicised.
Referencing Numbers
- To introduce cross-references, you can give the command \label{name} within the statement of a theorem, lemma, proposition or corollary in order assign the given name to that result.
- To reference the number assigned to that result in some other theorem, one gives the command \ref{name}; this will be replaced by the number automatically assigned by LaTeX to that result when the LaTeX program is executed.
- We recommend using consistent label names like eq:whatever and sec:whatever, but it is not required.
- The necessary space above and below the statement of the theorem will automatically be generated by LaTeX.
Example
\documentclass[12pt,letterpaper]{article}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\begin{document}
\section{Introduction}
Theorems can easily be defined:
\begin{theorem}
Let \(f\) be a function whose derivative exists in every point, then \(f\) is
a continuous function.
\end{theorem}
\begin{theorem}[Pythagorean theorem]
\label{pythagorean} % To introduce cross-references number
This is a theorem about right triangles and can be summarised in the next
equation
\[ x^2 + y^2 = z^2 \]
\end{theorem}
% to assign a referencing numbers
And a consequence of theorem \ref{pythagorean} is the statement in the next
corollary.
\begin{corollary}
There's no right rectangle whose sides measure 3cm, 4cm, and 6cm.
\end{corollary}
You can reference theorems such as \ref{pythagorean} when a label is assigned.
\begin{lemma}
Given two line segments whose lengths are \(a\) and \(b\) respectively there is a
real number \(r\) such that \(b=ra\).
\end{lemma}
Notes
- If you are using either packages with amsmath, you must load amsmath first, example:
- \usepackage{amsmath}
- \usepackage{amsthm}
- By default, each theorem-like uses its own counter. However it is common for similar types of theorems (e.g. Theorems, Lemmas and Corollaries) to share a counter.
- for above example "Theorem 1.2" \label{pythagorean}refers to the 2nd theorem in the 1st section of a document. In this case, specify the theorem in the preamble as follows:
There are three new environments defined in the preamble.
- \newtheorem{theorem}{Theorem}[section]
This is the example presented in the introduction but it has the additional parameter [section] that restarts the theorem counter at every new section. - \newtheorem{corollary}{Corollary}[theorem]
An environment called corollary is created, the counter of this new environment will be reset every time a new theorem environment is used. - \newtheorem{lemma}[theorem]{Lemma}
In this case, the even though a new environment called lemma is created, it will use the same counter as the theorem environment. In this case, define subsequent theorems from {theorem}.
Next Theorem and Proof In Latex 2 >>
Bibliography
http://www.mnstate.edu/ ( university )
http://www.ams.org/
https://www.tcd.ie/ ( university )
https://www.overleaf.com/
http://www.ntnu.no/ ( university )
https://en.wikibooks.org/
http://web.mit.edu/ ( university )
https://www.brown.edu/ ( university )
https://illinois.edu/ ( university )
https://www.impan.pl/ ( university )
latex document typeset, typesetting
