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Results tagged with gm.general-mathematics
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Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
78
votes
Conceptual reason why the sign of a permutation is well-defined?
This is obviously a subjective question, but I teach this in two phases
(1) I need to know this fact very early, so I give the quickest definition I know:
$$\mathtt{sign}(\sigma) = \frac{\prod_{i<j} \ …
- 156k
11
votes
A set for which it is hard to determine whether or not it is countable.
I'll be the obnoxious one: The set of subsets $S$ of $\{ x+iy \in \mathbb{C}, \ 1/2 < x < 1 \}$ such that $\zeta(s)$ restricted to $S$ is zero.
6
votes
Accepted
What is the rate of convergence?
Putting $x_n = 1+y_n$, we have $y_{n+1} = y_n + \frac{y_n^2}{2}$. There is a standard method for analyzing recursions of the form $y_{n+1} = y_n+O(y_n^2)$. A good introduction is chapter 8.4 in de Bru …
- 156k
4
votes
Why does $\sqrt 5$ occur in manageable situations of these scenarios?
$\def\QQ{\mathbb{Q}}$Three of these four examples involve $5$-fold symmetry. If $\zeta_5$ is a primitive $5$-th root of unity, then $\zeta_5 + \zeta_5^{-1} = \tfrac{1 \pm \sqrt{5}}{2}$. So any computa …
- 156k