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”|”. But it still carries the same meaning.

moreover

means satisfies the characteristic

**Different kinds of sets:**

**1.The empty set**

The set containing no elements at all is denoted:

**2.Integers**

Every number without a decimal or fractional part, denoted by

**3.Natural numbers**

Represents all nonnegative integers:

**4.Counting numbers**

All positive integers:

**5.Rational numbers**

Every integer that can be written in the form: where denoted by .

**6.Real numbers**

All the numbers on the number line, denoted by

**7.Irrational numbers**

Real numbers that cannot be written in the form where denoted by

**Intervals**

let and belong to , then

**Combining sets**

is all the elements in or

is all the elements in and

if

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.

Aidan HornFebruary 17, 2016 at 6:41 pmTry not putting in a return before and after all your Latex symbols. Can’t you just enclose them in [latex] some Latex code [/latex] within the same paragraph?

Tumelo LephadiFebruary 17, 2016 at 7:24 pmI tried doing that at first but then it didn’t work at all. Right now what I do is use this format $latex(code)$ and when I do that the latex code doesn’t fit in with the rest of the text. So I resorted to returning before and after each latex entry. I’ll try that method again though. Your input is appreciated.

UCT MAM1000 lecture notes subject links – MathemafricaJanuary 17, 2018 at 9:33 am[…] Sets […]