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Apr
16
answered Evaluating norm of the operator
Apr
13
reviewed Approve Lagrange multipliers in Calculus of Variations
Apr
13
reviewed Approve How to prove this inequality? $(a+b+c=1)$
Apr
13
comment Degree of an extension of $ \mathbb{Q} $
A basis of $\mathbb{Q}(\alpha)$ is given by the powers of $\alpha$ (up to the degree of the extension minus one).
Apr
13
reviewed Reject Showing $\sum\frac{\sin(nx)}{n}$ converges pointwise
Apr
13
reviewed Approve Eigenvectors belonging to different eigenvalues are linearly indepenent. Problem with proof.
Apr
12
comment A problem from Artin
To give you an intuition, the generator of $\ker \varphi$ will be the "simplest" polynomial equation satisfied by $x$ and $y$ if you set $x = t^2 - t$ and $y = t^3 - t^2$ (it amounts to the "simplest" Cartesian equation for the parametric curve $(x,y) = (t^2-t, t^3-t^2)$). Here we have $y = tx$, so $x = \left(\frac{y}{x}\right)^2 + \frac{y}{x}$. We multiply by $x^2$ to get a polynomial equation $x^3 - y^2 - xy = 0$. So $f = x^3 - y^2 - xy$ should be the generator of $\ker \varphi$.
Dec
14
comment Number of ways to choose 6 books out of 20 books such that no 2 are adjacent books
As I understand the solution, $1$ always denotes a pair (book, no book), except if for the last $1$ in the sequence (for example $101$ means (book, no book, no book, book) and $110$ means (book, no book, book, no book)). With this convention there is no ambiguity and no need for the $2$.
Oct
22
awarded  Nice Answer
Oct
13
reviewed Approve Understanding Borel sets
Sep
30
reviewed Approve Weird limit problem
Jun
13
reviewed Approve Intro to Real Analysis
Jun
5
comment Find the $f(x)$ from the given information
I have no idea if this might be useful, but if you denote $g(x) = \frac{x-1}{x}$ then $g^{-1}(x) = g(g(x)) = \frac{1}{1-x}$ and $g(g(g(x))) = x$.
Jun
5
reviewed Approve Understanding ω-consistent and ω-incomplete theory
Jun
5
reviewed Approve Taylor series for $\sinh1$
Jun
5
revised Find the $f(x)$ from the given information
added 11 characters in body
Jun
5
reviewed Edit Help me prove congruency
Jun
5
revised Help me prove congruency
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Jun
5
reviewed Reject Determining if certian properties of a topological space pass to its image under a quotient map.
Jun
5
reviewed Approve Help me prove congruency