Tag: Real numbers
- What Is a Number? From the Naturals to the Reals, and Why 1 = 0.999… Is TrueFollows the extension from the naturals to the reals through unsolvable equations, proves that the rationals have gaps, and derives 1 = 0.999… three ways from the completeness axiom.MathematicsFoundations of MathematicsUndergraduateReal numbersRational numbersIrrational numbersCompletenessInfinite decimals~15 min
- Is 1 Equal to 0.999…? Fixing the Meaning of an Infinite Decimal FirstWe examine 0.999… = 1 by first defining what an infinite decimal means, then carry the three classical arguments to completion and explain why intuition rebels.MathematicsMathematical ColumnsHigh school / generalReal numbersInfinite decimalsLimitsGeometric seriesDensity~11 min
Operated by: Mugen Giken LLC ・Pricing ・Terms ・Legal notice