# Important Sets

## Prerequisites

### Important Sets

#### Introduction

• Some sets are used so often in mathematics that they are given their own names.
• Z: The set of all integers.
• R: The set of all real numbers.

#### Integers

• The set of all integers contains all the whole numbers, including negative numbers and 0.
• It is represented by an uppercase bold (or blackboard bold) Z:
LaTeX:\mathbb{Z} = \{ ..., -3, -2, -1, 0, 1, 2, 3, ... \}

#### code (Python)

i = 1
print(type(i))  # prints <class 'int'>

#### Real Numbers

• The set of all real numbers contains every number that is not imaginary. This includes:
• Integers: e.g. 0, 1, 2
• Rational Numbers: Those which can be represented as a fraction, e.g. 0.5, 1.1
• Irrational Numbers: Those which cannot be represented by a fraction, e.g.
• It is represented by an uppercase bold (or blackboard bold) R:
LaTeX:\mathbb{R} = \{ -1, 1.4, \pi \}

#### code (Python)

Unfortunately we cannot represent irrational numbers using code. Instead we can approximate them as floating point numbers:
r = 1.41421356237
print(type(r))  # prints <class 'float'>