Newbetuts
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New posts in real-analysis
Can you please check my proof of this limit of derivative
real-analysis
proof-verification
Proving that $x^{\frac{1}{n}}$ is uniformly continuous over $[0, \infty)$ with the usual metric
real-analysis
epsilon-delta
uniform-continuity
Suppose $\sum a_n$ converges absolutely and $\sum b_n$ converges. Give an example where the Cauchy product does not converge absolutely.
real-analysis
sequences-and-series
cauchy-product
Elegant solution to $\lim\limits_{n \to \infty}{[n(\sqrt[n]{a} - 1)]}$
calculus
real-analysis
limits
alternative-proof
Why do non-constant periodic functions have no limit at infinity?
calculus
real-analysis
limits
Uniform convergence for sequences of functions
calculus
real-analysis
analysis
A continuous function with positive and negative values but never zero?
real-analysis
complex-analysis
Prove that if $f$ and $g$ are integrable functions on $[a, b]$ such that $f(x) = g(x)$ almost everywhere, then $\int^b_a f = \int^b_a g$
real-analysis
Solution to the functional equation $f(2x) = f(x)\cdot\sin(x)$?
real-analysis
functions
fourier-analysis
functional-equations
Machine Learning: Is the softmax function Lipschitz with Lipschitz constant $1$?
real-analysis
proof-verification
convex-optimization
machine-learning
lipschitz-functions
What are the conditions necessary and sufficient for a function $f : \mathbb{R} \to \mathbb{R}$ to be "represented by a graph"?
real-analysis
soft-question
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
calculus
real-analysis
multivariable-calculus
functions
inverse-function-theorem
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
real-analysis
summation
Does $\{f_ng_n\}\to fg$ uniformly?
real-analysis
sequences-and-series
general-topology
examples-counterexamples
uniform-convergence
Characterization of lim sup, lim inf
real-analysis
definition
limsup-and-liminf
On Lebesgue Outer Measure of an interval
real-analysis
measure-theory
compact Hausdorff space and continuity
real-analysis
general-topology
A problem on continuous functions
real-analysis
general-topology
continuity
Why can complex numbers be written in exponential form? $z=r(\cos \theta+i\sin \theta)$ is $z=re^{i\theta}$.
real-analysis
complex-numbers
How to construct a dense subset of $\mathbb R$ other than rationals.
real-analysis
general-topology
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