Module 1
:
Real Numbers, Functions and Sequences
Lecture
2
:
Convergent & Bounded Sequences [ Section 2.2 : Convergent Sequences ]
2.2.4
Theorem:
Limit a sequence is unique.
Proof:
Suppose
as well as
with
, say
.
Take
. Then by definition, there exists
such that
and
Thus, for
,
which is a contradiction. Hence,
.
Back
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as well as 
with 
, say 
.
. Then by definition, there exists 
such that 
,
. 
