Every Convergent Sequence is Bounded (Proof) | Real Analysis

In this video, we prove that every convergent sequence is bounded. It may seem obviously true, but analysis is all about being rigorous and careful. The proof is relatively straight forward to understand, but one that may seem a bit out of reach to try to come up with yourself. In analysis, this is normal! Just make sure you understand this proof and the intuition behind coming up with proofs will come naturally with time. Previous video on real analysis (limits of convergent sequences are unique): Next video :    • Equivalent Definitions of Convergence | Re...   Triangle inequality video:    • The Triangle Inequality (Derivation) | Rea...   Definition of convergence video:    • Convergence of Sequences - Formal (Quantif...   Boundedness video:    • Sequences and Boundedness of a Sequence | ...   Real analysis playlist:    • Real Analysis