/sci/ - Science & Math » Thread #12670011

825KiB, 1800x1108, 1555137200076.png

View Same Google iqdb SauceNAO

Anonymous Fri 05 Feb 12:31:56 2021 No.12670011 View Reply Original Report

Quoted By: >>12670800

Oldie but a goodie

Anonymous

Anonymous Fri 05 Feb 2021 18:11:12 No.12670800 Report

Quoted By: >>12670810

>>12670011
Isn't this trivial or am I missing something?
The vector space of polynomials with degree smaller or equal to 1999 is finite dimensional (2000 dimensional in fact) so all norms on it are equivalent. Therefore

$|p(0)| \leq \| p \|_\infty \leq C \| p \|_1$

q.e.d.

Anonymous

Anonymous Fri 05 Feb 2021 18:14:19 No.12670810 Report

Quoted By: >>12670842

>>12670800
The question wants a single C that works for all polynomials of degree 1999.

Anonymous

Anonymous Fri 05 Feb 2021 18:21:45 No.12670842 Report

Quoted By:

>>12670810
Yes and the equivalence of norms gives you one.
https://en.wikipedia.org/wiki/Norm_(mathematics)#Equivalence
You can even pick C=1.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches