Stating definitions and theorems

In rigorously structured mathematical documents, specific textual components, such as definitions, theorems, lemmas, examples, and remarks are often numbered for effective cross-referencing. This structured approach is prevalent in self-contained scientific works such as theses.

For example, let’s create a definition, a theorem along with its proof, a lemma, and an additional note. All of these elements will be automatically numbered to facilitate cross-referencing. Let’s apply this to the Pythagorean theorem we know from school geometry.

How to do it...

We’ll continue utilizing the amsmath package, specifically a part of it, the amsthm package. Here are the steps to follow:

1. As usual, start with a document class. For our recipe, the article class is sufficient:

   \documentclass{article}

2. Load the amsmath and amsthm packages:

   \usepackage{amsmath}
   \usepackage{amsthm}

3. Define a theorem environment with the internal...