|October 19th, 2016, 11:12 AM||#1|
Joined: Mar 2015
From: New Jersey
Nested open intervals
Why does the nested interval theorem require closed intervals?
Let ai and bi converge to a.
Lim (ai,bi)=(a,a) doesn't exist: a<x<a
Lim (ai,bi]=(a,a] doesn't exist: a$\displaystyle \leq$x<a
Lim [ai,bi]=[a,a] exists: a$\displaystyle \leq$x$\displaystyle \leq$a, x=a
|October 19th, 2016, 01:33 PM||#2|
Joined: May 2007
Since ai and bi both converge to a, then a is in the limit interval. (a,a) and (a,a] are both empty (do not contain a), so they are wrong.
|intervals, nested, open|
|Search tags for this page|
Click on a term to search for related topics.
|Thread||Thread Starter||Forum||Replies||Last Post|
|Open Set is Union of Disjoint Intervals||zylo||Real Analysis||29||September 5th, 2016 08:16 AM|
|Open Sets and Intervals||dpsmith||Real Analysis||10||September 1st, 2016 08:26 AM|
|How to simplify a nested sum?||Bromster||Real Analysis||1||July 7th, 2014 04:04 AM|
|does open in M imply open in A?||450081592||Real Analysis||0||October 31st, 2011 06:30 PM|
|Nested formulas?||arcaine01||Algebra||1||July 31st, 2009 11:38 PM|