/sci/ - Science & Math

>>15111219
[math]\dfrac{(-1)^n}{(-1)^n + n^a} \dfrac{n^a - (-1)^n}{n^a - (-1)^n} = \dfrac{(-1)^n n^a - 1}{n^{2a} + 1} = \dfrac{(-1)^n n^a}{n^{2a} + 1} - \dfrac{1}{n^{2a} + 1}[/math]. The first term always converges by alternating series and the second one only converges for [math]a > 0.5[/math]

>>14495069
[math]K[x] / (x^2 - a) \to Cl (V, q)[/math] is surjective, as you've already pointed out, and injective as a map between [math]K[/math] vector spaces, since [math]K[x] / (x^2 - a)[/math] has two dimensions and [math]1[/math] and [math]x[/math] have different images.
Injective as a map between vector spaces implies injective always, naturally.