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Number Theory
๐ข
Number Systems
๐Greece/Indiaยท500 BC
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๐ขNumber Systems
Natural, Integer, Rational, Irrational, Real and Complex โ the hierarchy of number systems
Key Facts
- 1Natural numbers (N): 1,2,3โฆ โ Integers (Z): โฆโ2,โ1,0,1,2โฆ โ Rational (Q): fractions
- 2Irrational numbers: ฯ, โ2, e โ cannot be expressed as fractions; non-terminating, non-repeating decimals
- 3Real numbers (R) = Rational + Irrational; Complex numbers (C): a+bi where i=โโ1
๐ก The discovery of irrational numbers (โ2 cannot be expressed as a fraction) was so shocking that ancient Greeks reportedly drowned its discoverer, Hippasus
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