Final Answers
© 2000-2021 Gérard P. Michon,
Ph.D.
Limits
Religions do a useful thing:
they narrow God to the limits of man.
Victor Hugo (1802-1885)
See also, on this site:
- Algebra.
- Analysis.
- Calculus.
- Topology.
- Power Series.
- Planar Curves.
- Infinite Products.
- Category Theory.
- Gamma Function.
- Differential forms.
- Functional Analysis.
- Limits in abstract topological spaces.
- Cauchy principal value of an integral.
- Asymptotic analysis and asymptotic series.
- Fourier transform and tempered distributions.
- Completeness in metric spaces and uniform spaces.
- Cauchy sequences help define real numbers rigorously.
- Numerical Constants: 0, 1, i, e, p, Ö2, f, g, z(3), ln(2), G, etc.
- Two decreasing divergent series may have a convergent minimum!
- At a jump, a Fourier series is the half-sum of its left and right limits.
- Gibbs phenomenon; 9% overshoot of partial Fourier series near a jump.
- Sum of a divergent series. Defined when partial sums have no finite limit.
- Uniform convergence of continuous functions makes the limit continuous.
- Circumference of an ellipse: 4 exact series, a dozen approximate formulas!
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