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๐Ÿ”ข
๐Ÿ”ข Number Theory

Number Systems

Natural, Integer, Rational, Irrational, Real and Complex โ€” the hierarchy of number systems

Greece/India ๐ŸŒ 500 BC Number Theory

Key Facts

  1. 1

    Natural numbers (N): 1,2,3โ€ฆ โ†’ Integers (Z): โ€ฆโˆ’2,โˆ’1,0,1,2โ€ฆ โ†’ Rational (Q): fractions

  2. 2

    Irrational numbers: ฯ€, โˆš2, e โ€” cannot be expressed as fractions; non-terminating, non-repeating decimals

  3. 3

    Real numbers (R) = Rational + Irrational; Complex numbers (C): a+bi where i=โˆšโˆ’1

๐Ÿ”ข Did you know? The discovery of irrational numbers (โˆš2 cannot be expressed as a fraction) was so shocking that ancient Greeks reportedly drowned its discoverer, Hippasus

Quick Reference

Category

Number Theory

Country

๐ŸŒ Greece/India

Year / Era

500 BC

About

Natural, Integer, Rational, Irrational, Real and Complex โ€” the hierarchy of number systems