Sequential characterisation of limits
For with , limits along the function and along sequences decide each other:
where , each lies in , and is not the constant sequence.
Lemma 2.6 (Sequential Characterisation of Limits)
Let . Let where is an accumulation point of . Then
with and is not the constant sequence.
Related
Stated in
- Lemma 2.6 (Sequential Characterisation of Limits)§2.1 Limits of Functions