๐ Classification of Numbers in Mathematics
Numbers are classified into different types based on their properties. Below is a structured breakdown:
๐ข 1. Natural Numbers (N) & Whole Numbers (W)
โ Natural Numbers (N): Counting numbers starting from 1.
๐ Examples: 1, 2, 3, 4, 5, โฆ
โ Whole Numbers (W): Natural numbers + 0.
๐ Examples: 0, 1, 2, 3, 4, โฆ
๐ข 2. Integers (Z)
โ Integers (Z): Whole numbers and their negatives.
๐ Examples: โฆ -3, -2, -1, 0, 1, 2, 3, โฆ
๐ก Fact: Every whole number is an integer, but not every integer is a whole number.
๐ข 3. Rational Numbers (Q)
โ Rational Numbers (Q): Numbers that can be written as a fraction (p/q), where:
- p and q are integers
- q โ 0
๐ Examples:
- 1/2
- 3/4
- 0.3333… = 1/3 (Repeating Decimal)
- 0.25 = 1/4 (Terminating Decimal)
๐ข 4. Irrational Numbers
โ Irrational Numbers: Cannot be written as fractions and have non-terminating, non-repeating decimals.
๐ Examples:
- ฯ = 3.1415926535… (never repeats)
- โ2 = 1.41421356…
๐ข 5. Real Numbers (R)
โ Real Numbers (R): All Rational and Irrational Numbers combined.
โ Represented on a number line.
โ Includes: Integers, fractions, terminating & repeating decimals, surds.
๐ก Fun Fact: Every number you’ve ever used in daily life is a Real Number!
๐ข 6. Prime & Composite Numbers
โ Prime Numbers: Divisible only by 1 and itself.
๐ Examples: 2, 3, 5, 7, 11, 13, 17, 19…
โ Composite Numbers: Have more than two factors.
๐ Examples: 4 (1,2,4), 6 (1,2,3,6), 8 (1,2,4,8)
๐ข 7. Even & Odd Numbers
โ Even Numbers: Divisible by 2.
๐ Examples: 2, 4, 6, 8, 10โฆ
โ Odd Numbers: Not divisible by 2.
๐ Examples: 1, 3, 5, 7, 9โฆ
๐ข 8. Complex Numbers (C)
โ Complex Numbers: Extend real numbers by including imaginary numbers (i), where iยฒ = -1.
๐ General form: (a + bi), where a, b are real numbers.
๐ Examples:
- 2 + 3i
- -5 + 4i
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