Lecture 2: Sets
List of the things I learnt today
- Definition of a set
- Different ways of representing a set
- Different kinds of sets
- Intervals
- Combinations of sets
- Set notation in functions
Definition of a set
A set is a collection of objects
Different ways of representing a set
Sets of objects are usually denoted by uppercase letters e.g.
let be the set of all odd numbers.The objects contained in a set are called elements which are denoted by lowercase letters e.g.
is an element of
.
A set can be represented in two ways:
1.List
The set above is an finite list, you can count the number of elements.
Is also a finite list. It’s important to present enough elements to produce a sequence if the use of ellipses is implemented for shorthand purposes.
This is an infinite set, you cannot count the number of elements in the set.
2. Set Builder Notation
In the example above is an element in the set
where
is a characteristic of the elements which are specific to set
or you can replace “:” with”|”.…