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)

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 Loga b = c
 * 1)  $$Log_{10} a = c$$ then Log 10a = c
 * 2)  $$Ln a = c$$ then Lna = c
 * 3)  $$Log a + Log b = Log ab$$
 * 4)  $$Log a - Log b = Log \frac{a}{b}$$