Numeric

Numeric_Classification

Classifying Numbers

  • Natural numbers are the numbers that begin with 1 i.e 1, 2, 3, 4, … and continue
    till ∞ (infinity)    .

  • Whole numbers are the numbers that begin with 0 i.e 0, 1, 2, 3, 4, … and continue
    till ∞ (infinity)    .

  • Integers are the set of positive and negative numbers that begin from -infinity and continue till +infinity. i.e from -∞ … 3, 2, 1, 0, 1, 2, 3, … ∞.

  • Rational numbers are the numbers that can be written as fractions ( numerator / denominator ) or ratio ( a / b ) of two integers. A rational number is terminating
    in nature. Example 2/5 i.e 0.4

  • Irrational numbers are the numbers that can be written as fractions ( numerator / denominator ) or ratio ( a / b ) of two integers. An irrational number is non-terminating and non-repeating in nature. Example : 22/7 or π (3.141592653589…)

  • Prime numbers are the numbers that have only 2 factors, 1 and the number itself.
    Example : 2, 3, 5, 7, 11, …

  • Real numbers are the numbers that can be plotted on a number line. Example 0, -2, 6, …

Numeric Algorithms

  1. Euler’s totient function
  2. Generating prime numbers using the prime sieve algorithm
  3. Euclid’s algorithm for finding the GCD of two numbers
  4. Finding factorials of a large number
  5. Fast exponentiations
  6. Doing multiplication and exponentiation under mudulo
  7. Generating Pythagorean triples
  8. Finding binomial coefficients
  9. Generating subsets using bitwise
  10. Generating subsets using permutations

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