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shintuku
  • Member for 4 years, 4 months
  • Last seen more than a month ago
4 votes
1 answer
256 views

Synthetic geometry: stereographic projections of $\mathbb{C}$ on Riemann sphere $\Sigma$ are inversions in sphere $K$ centered on $\infty$ of $\Sigma$

4 votes
1 answer
104 views

Metric spaces: equivalence of neighborhood definition of continuity with usual one. Don't we need a constraint asserting existence of neighborhoods?

4 votes
3 answers
219 views

Can you graph $y^{4}x^{3}+x^{4}-y=0$ without a computer?

3 votes
1 answer
244 views

Is the localization at a prime ideal of any polynomial ring always a valuation ring?

3 votes
1 answer
236 views

Proof verification: if $a_n, b_n>0$ and $\lim\limits_{n \to\infty} \frac{a_n}{b_n}=L_1$ with $L_1>0$, then if $\sum a_n$ converges, so does $\sum b_n$

3 votes
1 answer
52 views

Can we use the Lambert W solution $y=-3W(K_2x^{-4/3})$ instead of $y =-3W(\frac 1 3\sqrt[3]{-\frac{K_1}{x^4}})$ if we choose an appropriate constant?

3 votes
1 answer
212 views

Least squares: can't find why $SSR = a_1 \sum Y_i + b_1 \sum Y_i X_i - n\overline Y^2$. Would anyone have references?

3 votes
1 answer
145 views

Reference request: let $f:\mathbb{R}\to\mathbb{N}$ be onto. In ZF no $g:\mathbb{N}\to\mathbb{R}$ s.t. $f(g(b))=b$ for all $b\in\mathbb{N}$ exists

3 votes
2 answers
126 views

In general, for a graph of solutions to a differential equation is there a 3D graph s.t. these curves are its level curves? Then, what's this graph?

3 votes
1 answer
80 views

Prove$\lim \limits_{x \to \infty} e^{-Px}\int Q'(x)\frac{e^{Px}}{P} \ dx$ exists and find it, for constant $P>0$ and $Q'(x) \to 0$ as $x \to \infty$

3 votes
2 answers
236 views

Multiplication in synthetic geometry (example using geometrical circle inversion theorem)

2 votes
2 answers
420 views

Proof technique: Given vector subspaces $U$ and $W$, prove that $U + W = \{ ...\}$

2 votes
1 answer
77 views

Undo a weakened statement in sequent calculus later in the inferences

2 votes
1 answer
99 views

How do I designate the infimum of the union of an indexed family of sets of real numbers using set theory?

2 votes
1 answer
61 views

In terms of the logic of the proof, what is the difference between $a+b$ and $A+B$ in the proof that $\sup(A+B) = \sup A + \sup B$?

2 votes
1 answer
37 views

Prove $A_n = (-1, n)$ is an open cover of $[0, \infty)$. How can I guarantee $(-1, n), (-1, n+1), ...$ eventually encompasses $[0, \infty)$?

2 votes
1 answer
102 views

Prove that the infinite unordered sum $\sum_{i \in \mathbb{Z}} 2^{-|i|}$ converges to $3$ by definition. Stuck on last part.

2 votes
1 answer
838 views

Prove that the Jacobian matrix is the matrix representation of the derivative. Non-ambiguous statement for "is the matrix representation of"?

2 votes
1 answer
186 views

When first encountering a set of primitive inference rules, how do we approach the derivation of the very first derivable inference rules?

2 votes
3 answers
88 views

For two cyclic groups $\phi:C_4 \to C_3$ with $x^i \mapsto y^i$, we have $\phi(x^4)=\phi(x^0)=e$ but also $\phi(x^4) = y^4=y$. Where am I going wrong?

2 votes
1 answer
100 views

What can we say about $a_n = 0.9a_{n-1}+0.3\sqrt{a_{n-1}}$? [closed]

2 votes
1 answer
79 views

Need help identifying what sort of differential equation this is

2 votes
0 answers
93 views

Suppose $B$ lies over $A$, s.t. $A,B$ integral domains. Does this tell us anything about which homomorphisms from $A$ to a field we can extend to $B$?

1 vote
1 answer
104 views

What is the set $S$ of rings $R$ such that, for all rings $R'$, there is at most one nonzero homomorphism $R \to R'$?

1 vote
2 answers
211 views

Given an arbitrary composite elementary function, does there exist some method to give us an intuition of its graph?

1 vote
1 answer
65 views

Under which conditions is a variety approximated by approximations of its equation? eg: $y^{4}x^{3}+x^{4}-y=0$ approx. by $y^4+x=0;(xy)^3-1=0;x^4-y=0$

1 vote
0 answers
86 views

Is the localization of a polynomial ring at a prime ideal a valuation ring if and only if the prime ideal is principal?

1 vote
2 answers
69 views

Nullstellensatz proof: we have an isomorphism $\phi$ between al. closed $F$ and $F[x_1, ..., x_n]/m$. Why do we have $x_i - \phi^{-1}(x_i+m) \in m$?

1 vote
0 answers
169 views

Explicitly finding the elements of $\mathbb Z[i]/\langle 3+2i\rangle$ [duplicate]

1 vote
1 answer
80 views

Question about the proof that $A = B \implies \{A, B\} = \{A \}$