Tumelo Lephadi – Mathemafrica

Absolute values and inequalities

Things that I learnt today. Emphasis on the I, I couldn’t make for MAM1000W today.

Absolute value definition
Properties of absolute values
Rules for inequalities

Absolute value

The absolute value of a number represents the distance between that number and $0$ on the real number line. Absolute value of a number $n$ is denoted by $|n|$ which is equal to $\sqrt{n^{2}}$ which is from the distance formula. Since it is the distance between $0$ and $n$ Hence $|n|=n$ if $n \geq 0$ and $|n|=-n$ if $n < 0$

Properties of Absolute values

$|nm| = |n||m|$
$|\frac{n}{m}| = \frac{|n|}{|m|}, (m \neq 0)$
$|n^{m}| = |n|^{m}$

Let $n > 0$ then

$|m| = n \iff m = \pm{n}$
$|m| < n \iff -n < m < n$
$|m| > n \iff m > n, m < -n$

Rules for inequalities

if $n<m$ then $n+p<m+p$
if $n<m$ and $p<q$ then $n+p<m+q$
if $n<m$ and $p>0$ then $np<mp$
if $n<m$ and $p<0$ then $np>mp$
if $0<n<m$ then $\frac{1}{n}>\frac{1}{m}$

How clear is this post?

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By Tumelo Lephadi| February 18th, 2016|Uncategorized|1 Comment

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 $\mathit{A}$ be the set of all odd numbers.The objects contained in a set are called elements which are denoted by lowercase letters e.g. $\mathit{a}$ is an element of $\mathit{A}$ .

A set can be represented in two ways:

1.List

$\mathit{A}=\{a, b, c, d\}$

The set above is an finite list, you can count the number of elements.

$\mathit{B}=\{a, b, c, d,... t\}$

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.

$\mathit{C}=\{1, 2, 3, 5, 8,... \}$

This is an infinite set, you cannot count the number of elements in the set.

2. Set Builder Notation

$\mathit{D}=\{e \in \mathbb{R} : \mathit{C} (e) \}$

In the example above $e$ is an element in the set $\mathbb{R}$ where $\mathit{C} (e)$ is a characteristic of the elements which are specific to set $\mathit{D}$ or you can replace “:” with”|”.…

By Tumelo Lephadi| February 17th, 2016|Uncategorized|3 Comments

Lecture 1: Ways to represent a function.

So today we basically learnt about different ways to represent a function and we defined what a function is in detail.

First things first, what is a function?

A function is a rule that assigns each element x ( x being any independent variable ) in a set A exactly one element, f(x) ( f(x) being a dependent variable ) in a set B.

From that definition of a function we can now distinguish the different types of ways to represent a function.

I only know four ways, maybe there’s more… idk

algebraically, with the use of an equation
graphs
tables
or just in words

So we also learnt how to test if a graph represents a function. To do that you have to use the vertical line test. which means that anywhere within the domain of the graph if an x value has more than one f(x) value assigned to it then that graph does not represent a function.…

By Tumelo Lephadi| February 15th, 2016|Uncategorized|2 Comments

About Tumelo Lephadi

Absolute values and inequalities

Lecture 2: Sets

Lecture 1: Ways to represent a function.