Sets

tags: Mathematics

All Mathematics Formula by Abhyas here

Please see README if this is the first time you are here.

Definition

Well defined collection of Distinct Elements

Forms

Roaster Form

Elements are listed in a comma sperated list bounded within curly braces

Set Builder Form

Properties of the elements are defined in a particular form:

$A=\{x|x$ is a perfect square

$\}$ read as "A is a set of all those

$x$ such that

$x$ is a perfect square."

• $A$ is the name of set.
• Within curly braces:
  • $x$ is a varibale
  • "
    $x$ is a perfect sqare" is the condition
  • "
    $|$" (such that) seperated the variable from the condition

Symbols

• Sets are denoted by upper case letters. eg.
  $A,P$ etc.
• If
  $x$ belongs to A, this can be denoted by
  $x\in A$.
• If
  $x$ doesnot belong to A, this can be denoted by
  $x\notin A$

Notations

Natural Numbers

$\mathbb{N}=\{1,2,3,4,5,6,...\}$ upto infinity

${\mathbb{N}}_{100}=\{1,2,3,4,5,...,98,99,100\}$ upto 100

NOTE: 0 is not a Natural Number

Whole Numbers

$\mathbb{W}=\{0,1,2,3,4,...\}$ upto inifinite

NOTE: 0 is part of Whole Numbers

Integer

Set of all Integers:

$\mathbb{Z}=\mathbb{I}=\{0,\pm 1,\pm 2,\pm 3,\pm 4,\pm 5,...\}$

Set of all +ve Integers:

${\mathbb{Z}}^{\mathbb{+}}=\{1,2,3,4,5,6,7,...\}$

Set of all -ve Integers:

${\mathbb{Z}}^{\mathbb{-}}=\{-1,-2,-3,-4,-5,-6,-7,...\}$

Set of non-zero Integers:

${\mathbb{Z}}_0=\{\pm 1,\pm 2,\pm 3,\pm 4,\pm 5,...\}$

NOTE:

• Do not confuse with complex numebr
  $Z$.
• 0 is neither -ve nor +ve
• You can apply +ve, -ve and 0 on any other set. This was just easy to type. So no individual example for other sets. Plus doing so would make these notes too long.

Rational Numbers

Set of rational numbers:

$\mathbb{Q}=\{x|x=p/q$ and

$p,q\in I$ and

$q\ne 0\}$

Set of +ve, -ve and non zero:

${\mathbb{Q}}^{+}$,

${\mathbb{Q}}^{-}$ and

${\mathbb{Q}}_0$

Irrational Numbers

Set of Irratonal Numbers =

$\mathbb{R}-\mathbb{Q}$

Real Numbers

All numbers except complex numbers

Set of all real numbers:

$\mathbb{R}$

Licensing and Links

All Mathematics Formula by Abhays here

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.