Limit of a sequence
when there exists with for all .
Uniqueness
Proposition 5.19
Limits of sequences are unique.
Proof
Suppose and with , and set . For large both and hold, so
a contradiction. Hence the limit is unique.
Related
Stated in
- Definition 5.16 (Limit of a Sequence)§5.2 Sequences
- Proposition 5.19§5.2 Sequences