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Results tagged with real-analysis
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user 725007
For questions about real analysis, such as limits, convergence of sequences, properties of the real numbers, the least upper bound property, and related analysis topics such as continuity, differentiation, and integration.
1
vote
example of discontinuous function
consider the following function: let $f:\mathbb{R}^{2}\rightarrow\mathbb{R}$ be
$f\left(x,y\right)=\begin{cases}
1 & \sqrt{x}<y<2\sqrt{x}\\
0 & \text{else}
\end{cases}$
the directional derivatives at …
- 318
1
vote
0
answers
104
views
Proof Check - Diffeomorphism between subsets of $\mathbb{R}^n$
I would like to know if my proof to this statement is true:
Statement: Let $\mathbb{H}^n\subset\mathbb{R}^n$ be $\mathbb{H}^{n}=\left\{ \left(x_{1},\dots,x_{n}\right)\in\mathbb{R}^{n}\;\lvert\;x_{n}\ …
- 318
2
votes
0
answers
183
views
Proof Check - Thomae's function integrabilty
I'd like to know if my following proof for the integrabilty of Thomae's function in $[0,1]$ is correct:
recall that $T:[0,1]\rightarrow\mathbb{R}$ is defined as
$$T(x)=\begin{cases}
0 & x\in[0,1]\setm …
- 318