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