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What are numbers?

Numbers are mathematical objects used to quantify and measure quantities or magnitudes. They can be classified into different types based on their properties and characteristics. Here are some common types of numbers-

  1. Natural Numbers (ℕ): Also known as counting numbers, natural numbers are positive integers starting from 1 and increasing indefinitely (1, 2, 3, 4, …).

  2. Whole Numbers (ℤ⁺): Whole numbers include all natural numbers along with zero (0, 1, 2, 3, …).

  3. Integers (ℤ): Integers are positive, negative, or zero whole numbers (-3, -2, -1, 0, 1, 2, 3, …).

  4. Rational Numbers (ℚ): Rational numbers are numbers that can be expressed as a fraction of two integers where the denominator is not zero (e.g., 1/2, -3/4, 5, -2).

  5. Irrational Numbers: Irrational numbers cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions (e.g., π ≈ 3.14159, √2 ≈ 1.414).

  6. Real Numbers (ℝ): Real numbers include all rational and irrational numbers. They can be represented on a number line and include integers, fractions, decimals, and irrational numbers.

  7. Complex Numbers (ℂ): Complex numbers are numbers of the form a + bi, where “a” and “b” are real numbers, and “i” is the imaginary unit (√-1). Examples include 3 + 2i, -1 – i, etc.

  8. Prime Numbers: Prime numbers are natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and themselves (e.g., 2, 3, 5, 7, 11, …).

  9. Composite Numbers: Composite numbers are natural numbers that have more than two positive divisors (e.g., 4, 6, 8, 9, 10, …).

  10. Even and Odd Numbers: Even numbers are integers divisible by 2 (e.g., -4, -2, 0, 2, 4, …), while odd numbers are integers not divisible by 2 (e.g., -3, -1, 1, 3, 5, …).

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