Basic Mathematics
This document provides a basic introduction to Mathematics. It assumes that you have no prior knowledge of mathematics. By the end of this document, you will know enough mathematics to navigate this wiki.
Sets
A set is a group with objects. Sets can contain any number of objects.
To represent sets, we draw a Shape. While we can use any shape, we will use this shape below for now.
The image above also depicts what we call an empty set. An empty set is a set with no objects.
Recall, however, that sets are "groups with objects". To represent a set with an object inside, we draw an object inside the set.
In fact, sets can contain any number of objects. The image below shows a set with multiple objects in it.
The image above shows a set with multiple objects, but each individual object is the same. Sets do not need to contain objects that are all the same as one another. Sets may contain objects that are different from one another.
[set with objects that are different from one another]
Multiple sets can be defined at the same time. Each set may have the same or different amounts of objects inside them.
[multiple sets with objects]
Sets can even have sets inside them too! Note that the set inside is called a subset while the set containing the other set is called a superset.
[set inside another set]
Set Symbols
Instead of drawing a set with objects, we can use symbols to represent the exact same thing.
Set
The symbol for a set is surrounded by an opening bracket ({) and a closing bracket (}). Each object in the set is separated by a comma (,).
Empty Set
Represented with ∅ or { }.
Equals
Equals means two sets have the same number of objects
Numbers
A number is a symbol describing the quantity of a set. In other words, a number describes the number of objects in a set.
Arabic Numerals
Place Values
Number Line
An alternative way of viewing total number of objects in a set
Arithmetic
Arithmetic lets you perform operations on numbers.
Addition
Addition is an operation where the sum of two terms is taken. Addition is represented by the symbol "+"
Subtraction
Subtraction is an operation where the second term is taken from the first term. Subtraction is represented by the symbol "-"
Multiplication
Multiplication is an operation where the first term is added to 0 as many times as the value of the second term denotes. Multiplication can be represented by the symbols "X," or "*," or "⋅," or simply by omitting an operator such as XY=(X*Y)
Division
Modulo
Modulo is similar to division. However, it gives you the remainder.
Properties
Commutative Property
The commutative property dictates that for certain operators, the position of the terms does not affect the outcome.
Ordering
This section goes over ordered sets
Ordered Sets
Ordinal Numbers
| Number | English Word Equivalent |
|---|---|
| 0 | Zeroth |
| 1 | First |
| 2 | Second |
| 3 | Third |
| 4 | Fourth |
| 5 | Fifth |
| 6 | Sixth |
| 7 | Seventh |
| 8 | Eigth |
| 9 | Ninth |
| 10 | Tenth |
| 11 | Eleventh |
| 12 | Twelfth |
| 13 | Thirteenth |
| 14 | Fourteenth |
| 15 | Fifteenth |
| 16 | Sixteenth |
| 17 | Seventeenth |
| 18 | Eighteenth |
| 19 | Nineteenth |
| 20 | Twentieth |
If the number is greater than 20, look at the last digit. That will determine its suffix.
| Digit | Suffix |
|---|---|
| 0 | -th |
| 1 | -st |
| 2 | -nd |
| 3 | -rd |
| 4 | -th |
| 5 | -th |
| 6 | -th |
| 7 | -th |
| 8 | -th |
| 9 | -th |
Axioms
An axiom is a statement that is a universally recognized truth. That is, there is no need to prove that it is true. Rather, it is true, and there is no need to prove it.