Tag: Limits
- Limits and Continuity: Reading ε-δ as a Contract on ErrorDirichlet's function shows why 'approaches indefinitely' is no definition. From ε-δ alone we prove uniqueness, the algebra of limits, squeezing, continuity and uniform continuity.MathematicsCalculusUndergraduateLimitsContinuityEpsilon-deltaUniform continuity~14 min
- Why You Cannot Divide by Zero: Granting 0 a Reciprocal Collapses the Number System to a PointThe school rule 'never divide by zero' explained from the definition of division as the inverse of multiplication. 5÷0 has no solution, 0÷0 has too many, and granting 0 a reciprocal forces 1=0, wiping out every number.MathematicsMathematical ColumnsHigh school / generalDivision by zeroDivisionReciprocalLimits~21 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