Skip to content Skip to navigation


You are here: Home » Content » Functions and Continuity Definition of the Number π


Recently Viewed

This feature requires Javascript to be enabled.

Functions and Continuity Definition of the Number π

Module by: Lawrence Baggett. E-mail the author

Summary: An introduction, with links, to a subcollection about functions and continuity.

The concept of a function is perhaps the most basic one in mathematical analysis. The objects of interest in our subject can often be represented as functions, and the “ unknowns” in our equations are frequently functions. Therefore, we will spend some time developing and understanding various kinds of functions, including functions defined by polynomials, by power series, and as limits of other functions. In particular, we introduce in this chapter the elementary transcendental functions. We begin with the familiar set theoretical notion of a function, and then move quickly to their analytical properties, specifically that of continuity.

The main theorems of this chapter include:

  1. The Intermediate Value Theorem ((Reference)),
  2. the theorem that asserts that a continuous real-valued function on a compact set attains a maximum and minimum value ((Reference)),
  3. A continuous function on a compact set is uniformly continuous ((Reference)),
  4. The Identity Theorem for Power Series Functions ((Reference)),
  5. The definition of the real number π,π,
  6. The theorem that asserts that the uniform limit of a sequence of continuous functions is continuous ((Reference)), and
  7. the Weierstrass MM-Test ((Reference)).

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens


A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks