Open Closed Sets Limit Points

[the_Unbiased]

is limit point also an accumulation point?

[BretBenesh]

Hi Aakash,

We are in agreement. A point L CAN be a limit point, even if it is in A (see L4 in the above video). When I said "If L is in A, then L doesn't count, " I meant that there must be a point of A _different from L_ in the epsilon neighborhood.

Otherwise, the points in the closed set leading up to L3 would all be limit points, which we don't want. Indeed, EVERY point of A would be a limit point, since |a-a|=0 < epsilon for every a in A and positive epsilon.

[amitritupranjal]

I watch some videos.l understood so many things.Thanks

[BretBenesh]

As for L1, it has point of A (different from L1) in every epsilon neighborhood. In this particular case, the points are all to the right of L1, although this fact is not the important thing about limit points; all that matters is that there is always a different point of A really close (on either side) of L1.

[aakashsensei]

Sir I have a doubt here, u said L cannot be a limit point of set A if it belongs to that set A, how is L1 a limit point of that closed set ?

[pritamdas]

what does it mean by*a exceeds at the most a finite number of members of S*