Metamath Proof Explorer

Table of Contents - 17.1.1. Conventions

<p> This section describes the conventions we use. These conventions often refer to existing mathematical practices, which are discussed in more detail in other references. They are organized as follows: <ul> <li> conventions: general conventions</li> <li> conventions-labels: conventions related to labels</li> <li> conventions-comments: conventions related to comments</li> </ul> <p> Logic and set theory provide a foundation for all of mathematics. To learn about them, you should study one or more of the references listed below. We indicate references using square brackets. The textbooks provide a motivation for what we are doing, whereas Metamath lets you see in detail all hidden and implicit steps. Most standard theorems are accompanied by citations. Some closely followed texts include the following: <ul> <li>Axioms of propositional calculus - [Margaris].</li> <li>Axioms of predicate calculus - [Megill] (System S3' in the article referenced).</li> <li>Theorems of propositional calculus - [WhiteheadRussell].</li> <li>Theorems of pure predicate calculus - [Margaris].</li> <li>Theorems of equality and substitution - [Monk2], [Tarski], [Megill].</li> <li>Axioms of set theory - [BellMachover].</li> <li>Development of set theory - [TakeutiZaring]. (The first part of [Quine] has a good explanation of the powerful device of "virtual" or class abstractions, which is essential to our development.)</li> <li>Construction of real and complex numbers - [Gleason].</li> <li>Theorems about real numbers - [Apostol].</li> </ul>

  1. conventions
  2. conventions-labels
  3. conventions-comments