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Jul
20
answered $L^p$ and $\ell^p$ spaces
Jul
20
comment How to prove that $e^x$ is convex?
That's great and actually does not rely on derivative arguments: A function $f$ is convex if for every $x$ there exists $c$ such that for all $y$ it holds $f(y) \geq f(x) + c(y-x)$. You showed that $c=e^x$ works. This does not only show that $f$ is convex but also that $e^x$ is a subgradient of $\exp$ at $x$.)
Jul
20
comment How does the Vitali set violate the definition of measurable sets?
@avid19 The other argument goes more into the direction of the basic problem of measure. It shows that the unit interval can be partitioned into a countable number of sets that are basically cyclic translations of the Vitali sets and hence, there can be no countable additive and translation invariant measure for the Vitali set and the unit interval.
Jul
9
comment Becoming an Interuniversal Geometer
Go and read the first few pages of his papers, check the references in the paper in case you need clarification and then decide on your own.
Jul
7
comment Number of elements in a finite $\sigma$-algebra
The link is broken…
Jul
6
comment Operator Norm and Submultiplicativity against the Spectral Norm
Actually, the notion of operator norm depends of the chosen norms in the domain and the co-domain of the operator.
Jun
16
comment Please help: My MATLAB code for solving a 2D Schrödinger equation keep giving me weird output.
Probably the wrong forum… scicomp could be better. Anyway, the effect you see is due to a not well chosen discretization of the derivatives. Your dx and dy only use every other point and not the neighbouring point. Generally, the Laplace operator is div after grad and should be implemented as dx'*dx, i.e. using the adjoint derivative. In practice that means that you first use forward differences and then backward differences, ending up with a filter like [1 -2 1]/h^2.
Jun
2
reviewed Close confusing probability question - help!
Jun
2
reviewed Close Find the measure of the central angle with a radius of $13$ inches and the area of a sector measuring $42.25\pi$ square inches.
Jun
2
reviewed Close What is the moment generating function of Dirichlet distribution?
Jun
2
reviewed Close Need help with Mean Value Theorem Please!
Jun
2
reviewed Close Modular arithmetic: How do resolve it?
Jun
2
reviewed Close Finding a length in a circle
May
22
reviewed Close rearranging differential equations
May
22
reviewed Close The integer part of $x+1$ is the integer part of $x$ plus $1$
May
17
comment Intuition behind uniformly continuous functions
How does this heuristic work for $\sin(1/(x-1))$?
May
14
answered About window function
May
11
comment Continuity of $\frac{1}{|x|}$ at $x= 0$
You only need continuity at a single point and only get that. Your answer is totally, btw…
May
11
comment Continuity of $\frac{1}{|x|}$ at $x= 0$
More precisely: if $f$ is continuous at $x$ and $f(x)\neq 0$, then $1/f$ is continuous at $x$.
May
11
reviewed Reject Continuity of $\frac{1}{|x|}$ at $x= 0$