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19m
comment Proving that two arbitrary circles are homeomorphic
If they both have the origin in therir inside, yes
23m
comment Non-standard examples of Distributions
How about $\phi\mapsto\lim_{\epsilon\to 0^+}\left(\int_{-\infty}^{-\epsilon}\frac{\phi(x)}{x}\,\mathrm dx+\int_{\epsilon}^{\infty}\frac{\phi(x)}{x}\,\mathrm dx\right)$?
1h
answered Open Sets in the Extended Real Line
2h
answered Find smallest discrete logarithm, knowing some discrete logarithm.
2h
comment Find smallest discrete logarithm, knowing some discrete logarithm.
Any assumptions about $a$? Such as primitivity? Or at least $\gcd(a,m)=1$?
2h
revised How do I write this proof formally?
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2h
answered How do I write this proof formally?
3h
answered What is an example of transcendental extension such that a monomorphism cannot be extended?
3h
comment Approximation for the Summation of Sequence of Powers of Sines Functions.
@AhmedYounes Yes. For $k>1$, we have $\lim_{n\to\infty}\frac{\sin^n(z_k)}{\sin^n(z_1)}=0$
4h
comment Approximation for the Summation of Sequence of Powers of Sines Functions.
... where $\sin^n(z)$ is understood as $\underbrace{\sin(\sin(\cdots(\sin}_n(z)\cdots))$, not $\sin(z)\cdot\sin(z)\cdot\ldots\cdot \sin(z)$, I assum?
4h
answered Show that $N = f(M) \bigoplus N'$ if and only if there exists $\alpha: N \rightarrow M$ such that $\alpha(f(m)) = m$ for all $m \in M$.
4h
comment Is the null set $\emptyset$ a real subset of any set?
Possibly a translation problem? A proper subset of $A$ is a set $B$ with $B\subsetneq A$. With this definition $\emptyset$ is a proper subset of $A$ unless $A=\emptyset$
5h
answered How do I find all conjugates of $\sqrt{1+\sqrt{2}}$ over $\mathbb{Q}$?
19h
comment quick question about prime numbers and division
@Arthur But probably the OP's book is really referring to $n$ being irreducible ...
19h
answered Finding an ODE given some of its solutions
19h
comment Verifying linear independence for $\left\{ \sqrt{x} , \sqrt{x+1}, \sqrt{x+2} \right\}$ using Wronskian
@Dor Indeed, that seems to be a weird claim in your notebook. I'd double check their formulation (and their proof of the Wronskian test)
19h
revised Verifying linear independence for $\left\{ \sqrt{x} , \sqrt{x+1}, \sqrt{x+2} \right\}$ using Wronskian
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19h
revised Verifying linear independence for $\left\{ \sqrt{x} , \sqrt{x+1}, \sqrt{x+2} \right\}$ using Wronskian
added 6 characters in body
19h
comment Verifying linear independence for $\left\{ \sqrt{x} , \sqrt{x+1}, \sqrt{x+2} \right\}$ using Wronskian
My ODE is obtained from $y^2=x+c$, hence $(y^2)'=1$
19h
answered Verifying linear independence for $\left\{ \sqrt{x} , \sqrt{x+1}, \sqrt{x+2} \right\}$ using Wronskian