Lecture 1: Introduction

What is 2800 about?

How to succeed in 2800


\(\mathbb{N}\) is the set of natural numbers, \(\mathbb{N} = \{0, 1, 2, \dots\}\).

\(\mathbb{R}\) is the set of real numbers.

\(x \in X\) means that \(x\) is an element of the set \(X\).


Definition: A function is an unambiguous rule; for every input there should be an unambiguous output. The domain is the set of inputs. The codomain describes the type of outputs; there may be elements of the codomain that do not have an element of the domain that map to them. The image is the set of outputs that actually have an input mapped to them.

Note: Our definition of function corresponds to MCS's definition of total function.

Note: some books use "range" to mean "codomain", while others use "range" to mean "image". I try to avoid the term "range" to avoid ambiguity.

To specify a function, you must give the domain, codomain, and the rule.