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20h
revised How to show there exists $E$ such that $E \cap K_n$ is dense for every $n$?
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20h
comment How to show there exists $E$ such that $E \cap K_n$ is dense for every $n$?
@AsafKaragila : Right. I guess I need countable choice there? since I want a bijection $\varphi_n$ for each $n \in \mathbb N$. I never did set theory formally, I should get down to it someday..
1d
answered How to show there exists $E$ such that $E \cap K_n$ is dense for every $n$?
1d
revised $K$ is a region in $\mathbb{R}^2$ where the area is $5$
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1d
answered $K$ is a region in $\mathbb{R}^2$ where the area is $5$
2d
answered Number of functions for $(f(x))^2=x^2$
Apr
24
comment show the function is a homeomorphism?
@ThomasAndrews : Sure. I totally agree on your comment, I was just not thinking it through very much at the moment and simply answered.
Apr
24
comment show the function is a homeomorphism?
@greg : If you can't assume the Inverse Function Theorem (or if you don't know it), then of course my proof isn't of much help. The inverse function theorem in this case says that we can define the inverse function "locally", i.e. in the neighborhood of a point $p \in (-1,1)$, say $U$, there is a neighborhood of the point $f(p) \in \mathbb R$, say $V$, such that the restriction $f : U \to V$ is differentiable with differentiable inverse. But if you want the function explicitly it doesn't bring you anywhere close to computing anything.
Apr
24
comment show the function is a homeomorphism?
@ThomasAndrews : I agree it might be a sledgehammer, but I think it is okay to assume that the OP knows what differentiation means, and if he doesn't know what $C^1$ means he could have always commented but it would have indeed be nice of me to explicit it, although I didn't think of doing it in the first place.
Apr
24
answered show the function is a homeomorphism?
Apr
24
answered Finding the limit of a sequence of functions
Apr
24
comment Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction
@Zach466920 : At the moment where I wrote my comment, your approach did not seem clear at all ; now it is. I hadn't voted, for the record.
Apr
23
comment Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction
How is this even relevant? You're not considering the same sequence as in the question. The sequences $\sqrt{k+\sqrt{k+\cdots}}$ and $\sqrt{1+\sqrt{2+\cdots}}$ are not the same.
Apr
23
answered Can we say that $\sqrt{2}=2/(2/(2/(2/\ldots)))$?
Apr
23
revised $\int_a^{b} f(x) dx$ exists then so does $\int_{a+c}^{b+c} f(x-c)dx$
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Apr
21
comment Gorgeous diophantine equation
One question : Why this one?
Apr
20
answered Is $\sqrt[\beta]{\alpha}$ algebraic?
Apr
20
comment Kernel of a $R$-linear map is uniquely determined?
@PtF : It's like in any "universal" construction : free modules, free $k$-algebras, tensor products... etc. :P
Apr
20
revised Kernel of a $R$-linear map is uniquely determined?
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Apr
20
answered Kernel of a $R$-linear map is uniquely determined?