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

Root of Integer

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

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

Log of Integer

There exist $a^{c}=b$ then Log_a b = c

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