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Is there a limit in a point surrounded by a role?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Can a limit of a function that's defined only in one point exist?Is there any other name for limits?Multi-variable function is undefined at every point, then limit still may existformal definition of limit and approach from both sidesCan endpoints be local minimum?Help with using fundamental theorem of calculus?Trying to understand discontinuities and domainsContinuity of square root function at the first pointLimit of a function at a point in the domain of the function and/or the closure of the domain.Is $x^x$ continuous on negative integers?










0












$begingroup$


I've already seen when we do the limit of a point even if it is out of the domain, but if its surrounds too?
A function F that is not defined on a open interval
"I" = ]-1,1[
Exist the limit of F, as x aproaches 0?










share|cite|improve this question









$endgroup$











  • $begingroup$
    A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
    $endgroup$
    – Michael
    Mar 26 at 17:46











  • $begingroup$
    Do you know where you red this? I dont know how to search this in the web,
    $endgroup$
    – Leo Martos Barbosa
    Mar 26 at 18:00










  • $begingroup$
    Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
    $endgroup$
    – Michael
    Mar 26 at 21:35















0












$begingroup$


I've already seen when we do the limit of a point even if it is out of the domain, but if its surrounds too?
A function F that is not defined on a open interval
"I" = ]-1,1[
Exist the limit of F, as x aproaches 0?










share|cite|improve this question









$endgroup$











  • $begingroup$
    A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
    $endgroup$
    – Michael
    Mar 26 at 17:46











  • $begingroup$
    Do you know where you red this? I dont know how to search this in the web,
    $endgroup$
    – Leo Martos Barbosa
    Mar 26 at 18:00










  • $begingroup$
    Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
    $endgroup$
    – Michael
    Mar 26 at 21:35













0












0








0





$begingroup$


I've already seen when we do the limit of a point even if it is out of the domain, but if its surrounds too?
A function F that is not defined on a open interval
"I" = ]-1,1[
Exist the limit of F, as x aproaches 0?










share|cite|improve this question









$endgroup$




I've already seen when we do the limit of a point even if it is out of the domain, but if its surrounds too?
A function F that is not defined on a open interval
"I" = ]-1,1[
Exist the limit of F, as x aproaches 0?







calculus






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 26 at 17:27









Leo Martos BarbosaLeo Martos Barbosa

115




115











  • $begingroup$
    A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
    $endgroup$
    – Michael
    Mar 26 at 17:46











  • $begingroup$
    Do you know where you red this? I dont know how to search this in the web,
    $endgroup$
    – Leo Martos Barbosa
    Mar 26 at 18:00










  • $begingroup$
    Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
    $endgroup$
    – Michael
    Mar 26 at 21:35
















  • $begingroup$
    A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
    $endgroup$
    – Michael
    Mar 26 at 17:46











  • $begingroup$
    Do you know where you red this? I dont know how to search this in the web,
    $endgroup$
    – Leo Martos Barbosa
    Mar 26 at 18:00










  • $begingroup$
    Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
    $endgroup$
    – Michael
    Mar 26 at 21:35















$begingroup$
A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
$endgroup$
– Michael
Mar 26 at 17:46





$begingroup$
A limit point x of a set needs to have points of the set that are different from it, but are arbitrarily close to it. If there are no other points of the set within a neighborhood of x then x is not a limit point of that set. Even so , if x is itself a member of the set then the sequence x,x,x,... is indeed a sequence of points in the set that converges to x.
$endgroup$
– Michael
Mar 26 at 17:46













$begingroup$
Do you know where you red this? I dont know how to search this in the web,
$endgroup$
– Leo Martos Barbosa
Mar 26 at 18:00




$begingroup$
Do you know where you red this? I dont know how to search this in the web,
$endgroup$
– Leo Martos Barbosa
Mar 26 at 18:00












$begingroup$
Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
$endgroup$
– Michael
Mar 26 at 21:35




$begingroup$
Here is a description of "limit point" in wikipedia: en.wikipedia.org/wiki/Limit_point
$endgroup$
– Michael
Mar 26 at 21:35










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