Tag: Irrational numbers
- Techniques of Proof: Why Induction and Contradiction Are ValidWhy induction is valid, how it breaks without a base case, how proof by contradiction differs from contraposition, and two proofs that no rational number squares to 2.MathematicsFoundations of MathematicsUndergraduateMathematical inductionProof by contradictionContrapositionPeano axiomsIrrational numbers~29 min
- 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
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