# Arithmetic Course/Types of Number/Integer Number

## Integer Number

Integer number is a set of Positive Integer , 0 and Negative Integer

1. Positive Integer . +N > 0 = {+1,+2,+3,+4,+5,+6,+7,+8,+9}
2. Negative Integer . -N < 0 = {-1,-2,-3,-4,-5,-6,-7,-8,-9}
3. Zero . N = 0

## Properties

1. a + b = b + a
2. a + b + c = (a + b) + c = a + (b + c)

## Mathematic Operations

### Integer Addition

1. a + 0 = a
2. a + a = 2a
3. a + (-a) = 0

### Integer Subtraction

1. a - 0 = a
2. a - a = 0
3. a - (-a) = 2a

### Integer Multiplication

1. a x 0 = 0
2. a x a = a2
3. a x (-a) = -a2

### Integer Division

1. a / 0 = ∞
2. a / a = 1
3. a / (-a) = -1

### Multiple of Integer

a + a + a + .... = na
1. na + ma = an[1 + a^(m-n)]
2. na - ma = an[1 - a^(m-n)]
3. na x ma = (nm) a
4. na / ma = (n/m) a

### Power of Integer

a x a x a x .... = an
1. ${\displaystyle a^{0}=1}$
2. ${\displaystyle a^{1}=a}$
3. ${\displaystyle a^{-}1={\frac {1}{a}}}$
4. ${\displaystyle a^{n}+a^{m}=a*(m+n)}$
5. ${\displaystyle a^{n}-a^{m}=a*(m-n)}$
6. ${\displaystyle a^{n}\times a^{m}=a^{(m+n)}}$
7. ${\displaystyle {\frac {a^{n}}{a^{m}}}=a^{(m-n)}}$

### Root of Integer

There exist ${\displaystyle a^{n}=b}$  then ${\displaystyle {\sqrt {b}}=a}$

1. ${\displaystyle {\sqrt {0}}=0}$
2. ${\displaystyle {\sqrt {1}}=1}$
3. ${\displaystyle {\sqrt {-1}}=i}$
4. ${\displaystyle {\sqrt {a}}\times {\sqrt {b}}={\sqrt {ab}}}$
5. ${\displaystyle {\sqrt {a}}\times {\sqrt {b}}={\sqrt {ab}}}$

### Log of Integer

There exist ${\displaystyle a^{c}=b}$  then Loga b = c

1. ${\displaystyle Log_{10}a=c}$  then Log 10a = c
2. ${\displaystyle Lna=c}$  then Lna = c
3. ${\displaystyle Loga+Logb=Logab}$
4. ${\displaystyle Loga-Logb=Log{\frac {a}{b}}}$