Uniqueness of sequence limit

Question

The original poster here (I think) assumes that $L\ne M$, so essentially, $\lim _{n\rightarrow\infty}a_n\in\{L,M\}$. But OP assumes in his proof at one point that $\lim _{n\rightarrow\infty}a_n=L$. Is that okay?

I have this question because in answer by Andres Nicolas, it is said that if we have proved relevant result about the limit of a sum, or difference, the proof by OP is fine.

No his proof is not correct,because he assumed a priori that $L \neq M$ — Marios Gretsas, Aug 16 '17 at 12:18

score 1 · Answer 1 · answered Aug 16 '17 at 12:30

1

No, it is false. In analogy the proof runs as follows: If $a=b$ and $a=c$, then $b-c = a-a = 0$, so $b = c$. This does not utilize the notion of limit.

answered Aug 16 '17 at 12:30

Yes

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Uniqueness of sequence limit

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