# Fundamental Mathematics/Algebra

## Number Systems

 Algebra number system Egytian's number system use digits from 0-9 N10 = {0,1,2,3,4,5,6,7,8,9} Roman's number system use letters I , V , X , L , M , C

## Number Types

From divisibility

A number which can be divided by 2 without remainder is called an Even number.

$\mathbb {2N} =\{0,2,4,6,8...\}$ A number which cannot be divided by 2 without remainder is called an Odd number.

$\mathbb {2N+1} =\{1,3,5,7,9...\}$ A number, greater than 1, which can be divided by 1 and itself without remainder (aka a number with exactly 2 natural factors) is called a Prime number.

$\mathbb {P} =\{2,3,5,7,11...\}$ ## Algebra operations

Operation Arithmetic
Example
Algebra
Example
≡ – means "equivalent to"
≢ – means "not equivalent to"
Addition $(5\times 5)+5+5+3$ equivalent to:

$5^{2}+(2\times 5)+3$ $(b\times b)+b+b+a$ equivalent to:

$b^{2}+2b+a$ {\begin{aligned}2\times b&\equiv 2b\\b+b+b&\equiv 3b\\b\times b&\equiv b^{2}\end{aligned}} Subtraction $(7\times 7)-7-5$ equivalent to:

$7^{2}-7-5$ $(b\times b)-b-a$ equivalent to:

$b^{2}-b-a$ {\begin{aligned}b^{2}-b&\not \equiv b\\3b-b&\equiv 2b\\b^{2}-b&\equiv b(b-1)\end{aligned}} Multiplication $3\times 5$ or

$3\ .\ 5$ or   $3\cdot 5$ or   $(3)(5)$ $a\times b$ or

$a.b$ or   $a\cdot b$ or   $ab$ $a\times a\times a$ is the same as $a^{3}$ Division   $12\div 4$ or

$12/4$ or

${\frac {12}{4}}$ $b\div a$ or

$b/a$ or

${\frac {b}{a}}$ ${\frac {(a+b)}{3}}\equiv {\tfrac {1}{3}}\times (a+b)$ Exponentiation   $3^{\frac {1}{2}}$ $2^{3}$ $a^{\frac {1}{2}}$ $a^{3}$ $a^{\frac {1}{2}}$ is the same as ${\sqrt {a}}$ $a^{3}$ is the same as $a\times a\times a$ • Algebra
• Algebra