Number Systems, Sets, Unions, And Ordering

Definition 1) Number Systems

Number Systems are a way we categorize numbers. The categorization of certain numbers will make solving math problems later on Easier!

Examples :

$\mathbb{N}=\{1,2,3,...\}$

b) Whole Numbers :

${\mathbb{N}}_0=\{0,1,2,...\}$

c) Integers:

$\mathbb{Z}=\{...,-2,-1,0,1,2,\}$

d) Rational numbers:

$\mathbb{Q}=\{\frac{a}{b}\}$, “fraction” ex) $\frac{3}{5},5=\frac{5}{1}=\frac{10}{2},0.\overline{3}=\frac{1}{3}$

e) Irrational Numbers:

$\mathbb{R}\setminus \mathbb{Q}$, “Irrational numbers” ex) $\pi =\mathrm{3.14...}$, $e=2.718$, $\sqrt{2}=1.414$

f) Real Numbers:

$\mathbb{R}$, “A combination of both rational and irrational numbers”

g) Complex Numbers

$\mathbb{C}$, “The real numbers with the addition of an “imaginary number”. usually denoted as $i=\sqrt{-1}$”

• Note : The complex numbers are way above the scope of these notes, but do fill in many holes that we will discover throughout these notes. If you have the alloted free time to learn more about it, I reccomend starting with this varitassium Video