List of the things I learnt today
- Definition of a set
- Different ways of representing a set
- Different kinds of sets
- 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:
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”|”. But it still carries the same meaning.
means satisfies the characteristic
Different kinds of sets:
1.The empty set
The set containing no elements at all is denoted:
Every number without a decimal or fractional part, denoted by
Represents all nonnegative integers:
All positive integers:
Every integer that can be written in the form: where denoted by .
All the numbers on the number line, denoted by
Real numbers that cannot be written in the form where denoted by
let and belong to , then
is all the elements in or
is all the elements in and
then and are called a disjoint.
Set notation in functions
means that every element in the set is assigned to an element in the set by the function .
My first time using LaTeX. And I survived the fires of UCT.