Prove Lower Continuity Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Upper semi-continuity and lower semi-continuity of particular functions$limsup$ and cluster pointsTwo questions on $limsup$: do nested ones commute and sending $n$ to $-infty$How to prove sin(sin(sin…(sin(1))) converges to 0 without using continuity?Prove intersection of open balls is another open ballFind $ limsup_nto infty(frac2^nn!) $Uniform continuity, a direct proofShow that open rectangle is open set in metric space $(mathbbR^n, d_2)$Upper Limit DefinitionLower limit of a real function
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Prove Lower Continuity
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Upper semi-continuity and lower semi-continuity of particular functions$limsup$ and cluster pointsTwo questions on $limsup$: do nested ones commute and sending $n$ to $-infty$How to prove sin(sin(sin…(sin(1))) converges to 0 without using continuity?Prove intersection of open balls is another open ballFind $ limsup_nto infty(frac2^nn!) $Uniform continuity, a direct proofShow that open rectangle is open set in metric space $(mathbbR^n, d_2)$Upper Limit DefinitionLower limit of a real function
$begingroup$
Show that $limsup_x→x0 f(x) := sup_xn→x0 limsup_n→∞ f(x_n)$
I saw this line listed as a definition as I was reading http://webdoc.sub.gwdg.de/ebook/serien/e/reports_Halle-Wittenberg_math/05-04report.pdf.
However, this is not the definition I learned so I was wondering if the standard definition of $limsup_x→x0 f(x)$ of using open ball to define as r approaches 0 is reltaed to this definition and how I would prove it.
real-analysis sequences-and-series limits
asked Mar 27 at 2:25
james blackjames black
424114
$endgroup$
add a comment |
$begingroup$
Show that $limsup_x→x0 f(x) := sup_xn→x0 limsup_n→∞ f(x_n)$
I saw this line listed as a definition as I was reading http://webdoc.sub.gwdg.de/ebook/serien/e/reports_Halle-Wittenberg_math/05-04report.pdf.
However, this is not the definition I learned so I was wondering if the standard definition of $limsup_x→x0 f(x)$ of using open ball to define as r approaches 0 is reltaed to this definition and how I would prove it.
real-analysis sequences-and-series limits
asked Mar 27 at 2:25
james blackjames black
424114
$endgroup$
add a comment |
$begingroup$
Show that $limsup_x→x0 f(x) := sup_xn→x0 limsup_n→∞ f(x_n)$
I saw this line listed as a definition as I was reading http://webdoc.sub.gwdg.de/ebook/serien/e/reports_Halle-Wittenberg_math/05-04report.pdf.
However, this is not the definition I learned so I was wondering if the standard definition of $limsup_x→x0 f(x)$ of using open ball to define as r approaches 0 is reltaed to this definition and how I would prove it.
real-analysis sequences-and-series limits
asked Mar 27 at 2:25
james blackjames black
424114
$endgroup$
Show that $limsup_x→x0 f(x) := sup_xn→x0 limsup_n→∞ f(x_n)$
I saw this line listed as a definition as I was reading http://webdoc.sub.gwdg.de/ebook/serien/e/reports_Halle-Wittenberg_math/05-04report.pdf.
However, this is not the definition I learned so I was wondering if the standard definition of $limsup_x→x0 f(x)$ of using open ball to define as r approaches 0 is reltaed to this definition and how I would prove it.
real-analysis sequences-and-series limits
real-analysis sequences-and-series limits
asked Mar 27 at 2:25
james blackjames black
424114
asked Mar 27 at 2:25
james blackjames black
424114
asked Mar 27 at 2:25
james blackjames black
424114
asked Mar 27 at 2:25
james blackjames black
424114
asked Mar 27 at 2:25
james blackjames black
424114
424114
add a comment |
add a comment |
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