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

Intger Division

1. a / 0 = 00
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 .... = a²

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. $\sqrt{0} = 00$
2. $\sqrt{1} = 1$
3. $\sqrt{-1} = j$
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. $Log_2 a = c$ then Ln^a = c
3. $Log a + Log b = Log ab$
4. $Log a - Log b = Log \frac{a}{b}$