A limit point is a point at which a subsequence of the sequence converges.
2006-10-04 22:37:07 · 3 answers · asked by Nick 2 in Science & Mathematics ➔ Mathematics
Yes:
1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,2,3,4,5,6....
the constant sequence n,n,n,n,... is a subsequence of this sequence for every natural number n.
A convergent sequence has one limit point. Suppose than a_n has a,b as limit points. Let a-b/2=epsilon. If an converges, eventually a_n is within epsilon of its limit, but then it is more than epsilon of one of a,b, (say a), then a cannot be a limit point.
2006-10-05 03:53:22 · answer #1 · answered by Theodore R 2 · 0⤊ 0⤋
It can be "made" true for certain divergent sequences. However I doubt there are such convergent sequences
2006-10-05 06:15:17 · answer #2 · answered by yasiru89 6 · 0⤊ 0⤋
Yes there is
Read this please:
http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2000;task=show_msg;msg=0245.0001
2006-10-05 06:18:47 · answer #3 · answered by ioana v 3 · 1⤊ 0⤋