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Studying maths in a higher semester.


12h
comment Is There An Injective Cubic Polynomial $\mathbb Z^2 \rightarrow \mathbb Z$?
@mick You could "favourite" the question by clicking the star below the voting arrows. This will make the system notify you on updates to the question ;
14h
comment Question concerning one rule of the topological calculus in terms of the interior operator
+1 for using standard notation
14h
comment weak* convergence for sequence in $ L^\infty$
First prove this for hypercubes $\Omega = \prod_{i=1}^d (a_i, b_i)$, then try to generalise using that every bounded open set in $\mathbb R^d$ can be exhausted by open hypercubes.
14h
answered What can we say about output of Gram–Schmidt process
14h
comment What can we say about output of Gram–Schmidt process
@quid I put them on now, thanks :) cf. picture of proof (phunny)
14h
comment Does every isomorphism between $V$ and $V^*$ send some basis to its dual basis?
@AlexG. No your observation is correct. Only symmetric bilinear forms (and exactly these) can be unitariyly diagonalized.
14h
revised Solve the Diophantine equation $y^3=4x^2+4x+5$ in $x,y\in\mathbb{Z}$
added 28 characters in body
14h
comment What can we say about output of Gram–Schmidt process
@alex Because $\hat x_n$ is linearly dependent on all other $\hat x_i$ and yet must be orthogonal to all of them.
20h
comment How to show that the following relation is not an equivalence relation?
For completeness, $d(e_1,e_2) = \sqrt2$, $d(0,e_i) = 1$
20h
comment Why $1$ isn't a prime?
@user170039 Since your comment got upvoted, I added a small comment to each point telling exactly what goes nuts.
20h
revised Why $1$ isn't a prime?
added 123 characters in body
20h
revised Why $1$ isn't a prime?
added 123 characters in body
20h
comment Why $1$ isn't a prime?
@user170039 This is a list for both questions. Point 3. especially is an example for question 2., Points 1. and 2. are theorems answering question 1.
20h
answered Why $1$ isn't a prime?
21h
comment Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$
What ensures us that degree-$1$ Taylor preserves the limit? (curious)
21h
comment Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$
@Nick Please neither use displaystyle maths (\displaystyle, \dfrac) nor MathJax-only titles. Both are discouraged. The former because it costs much more front-page space and the latter due to technical reasons (Users unable to invoke the browser context-menu on the link)
21h
revised Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$
edited title
21h
comment How the cardinality of $\mathbb{R^+}$ and $\mathbb{R}$ same?
@JMoravitz Actually you showed $\mathrm{card}(\mathbb N)\le \mathrm{card}(\mathbb N)$ since this is an injection from $\mathbb N$ into $\mathbb N$ ;)
21h
answered Epimorphism of linear transformation
21h
comment Epimorphism of linear transformation
You should write up your definition of epimorphism first.