Definition
Limit (Sequence)
A real number
is called limit of sequence if almost all sequence elements lie within every epsilon neighbourhood of : A number
is thus the limit of a sequence if the following holds: Given any distance , an index can be found such that from this index onward, all sequence elements have a from/to that is smaller than . Such an must exist for every , no matter how small is chosen. If there exists an epsilon neighbourhood of
that does not contain infinitely many sequence elements, then cannot be the limit, then cannot be the limit of that sequence. Every limit is a limit point of that sequence.