Prove that any limit point is between lim inf A and lim sup A.
Thanks
Also if you could help me find an example of a sequence with 3 limit points that would be helpful.
2026-04-03 14:01:18.1775224878
Limit Points and lim inf and lim sup
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By definition limsup is the supremum (smallest upper bound) of all limit points and the liminf is the infimum (largest lower bound) of all limit points. Therefore, by definition of upper and lower bound, all limit points must be between the limsup and liminf. As for the sequence, the sequence A:=-1,0,1,-1,0,1,-1,0,1,... will work. limsup A=1 Liminf A=-1 but you could also construct a sub sequence that converges to 0 so 0 is also a limit point.