From English Wikipedia @ Freddythechick
This template must be substituted. Replace {{Archive header with {{subst:Archive header.
{| width = "100%"
|-
! colspan="3" align="center" | Mathematics desk
|-
! width="20%" align="left" | < February 26
! width="25%" align="center"|<< Jan | February | Mar >>
! width="20%" align="right" |Current desk >
|}
| Welcome to the Wikipedia Mathematics Reference Desk Archives
|
| The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.
|
February 27
Fully faithful endofunctors of Set
Does there exist a fully faithful endofunctor F of the category of sets that is not an equivalence? GeoffreyT2000 (talk) 17:06, 27 February 2019 (UTC)
- I don't think so? This is off the cuff, and I haven't taken the time to check it, but: Take a one-element set x. F must send it to a one-element set y. Now for any set z, by matching morphisms from x to z with morphisms from y to F(z), you should be able to understand the action of F on z as a bijection, which should then let you put together an inverse.--2404:2000:2000:5:0:0:0:C1 (talk) 22:55, 28 February 2019 (UTC)
Series
How I calculate value of x.?!! If S was known. — Preceding unsigned comment added by 151.236.179.162 (talk) 18:32, 27 February 2019 (UTC)
- Pretty sure the RHS is ζ(-log x) where ζ is the Riemann zeta function. I don't know if there are ways to compute ζ-1 that are an improvement over standard numerical root-finding algorithms. For values of S like π2/6, which is known to be ζ(2), x would be easy to find. --RDBury (talk) 21:09, 27 February 2019 (UTC)
