wicked dust
I´m currently stuck on this problem. It's clear to me that the pointwise limit doesn't exist for x in (0,2pi). My issue relays on finding an approach to do this. I've been thinking of using subsequences to get to the contradiction, but I'm not sure of the pattern they should be following and what would be my objetive.
hushed harborBOT
muted vapor
You should check convergence for x = 0 and x = 2pi first
And then split up the subsequences where the sequence gets very close to 1 and the other very close to -1
wicked dust
I mean for the values that aren’t 0 and 2pi, this is because of the oscillation
wicked dust
And then split up the subsequences where the sequence gets very close to 1 and t...
This is the step that’s giving me a headache, I’m not really sure of how to define these subsequences
What property they should accomplish
muted vapor
You want nx roughly equal to 2pi times an integer and nx roughly equal to pi + 2pi times an integer
lethal perch
I´m currently stuck on this problem. It's clear to me that the pointwise limit d...
If t=x/(2pi) is irrational then the set (t n)mod 1 is dense, so you can choose two subsequences of n such that (x n)mod 2pi tends to 0 and pi, thus giving cosine 1 and -1. If t is rational, say t=p/q, then you can also choose two subsequences, say n=qk and n=m+qk, where mp=1 (mod q).