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Results tagged with real-analysis
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user 88133
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
32
votes
Accepted
Is every real number in [0,1] a product of three (or more) Cantor set's numbers?
Yes, every real number $u \in [0,1]$ can be written as $u = x^2 y$ where $x,y \in C$ are in the Cantor set $C$. In particular, every real number in $[0,1]$ is a product of three Cantor set elements. T …
- 6,237
5
votes
Reference request: A multidimensional generalization of the fundamental theorem of calculus
The $p=2$ dimensional case is an exercise in Rogawski's calculus textbook. It is exercise 47 on page 885, section 15.1 (Integration in Several Variables) in the 2008 Early Transcendentals edition.
- 6,237
1
vote
About local maxima of multivariable polynomials
The set of critical points (in the domain) of a polynomial is the solution set of a system of polynomial equations viz the vanishing of the first derivatives. So it has finitely many irreducible compo …
- 6,237