Arithmetic Course/Types of Number/Integer Number

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Integer Number[edit]

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[edit]

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

Mathematic Operations[edit]

Integer Addition[edit]

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

Integer Subtraction[edit]

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

Integer Multiplication[edit]

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

Intger Division[edit]

  1. a / 0 = 00
  2. a / a = 1
  3. a / (-a) = -1

Multiple of Integer[edit]

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[edit]

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[edit]

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[edit]

There exist a^c  = b then Loga b = c

  1. Log_10 a = c then Log 10a = c
  2. Log_2 a = c then Lna = c
  3. Log a + Log b = Log ab
  4. Log a - Log b = Log \frac{a}{b}