Proof: The Limit of a Sequence is Unique | Real Analysis

A convergent sequence converges to exactly one limit. That is, the limit of a sequence is unique. We'll prove this by contradiction in today's real analysis video lesson. We assume our convergent sequence converges to a and b, and that they are distinct, as in the limit is not unique. We then pick a sufficiently small epsilon and apply the definition of convergence to force the terms of our sequence to eventually satisfy two contradictory inequalities.
Real Analysis Playlist: • Real Analysis
Intro to Sequences: • Intro to Sequences | C...
Definition of the Limit of a Sequence: • Definition of the Limi...
Proof (-1)^n Diverges: • Proof: Sequence (-1)^n...
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