We prove the results on the algebra of convergent sequences.
Many may look down upon or ignore this part of analysis. It happens in many courses in analysis. Teachers and students alike are too eager to launch into continuity, compactness etc. I recommend that you watch it with rapt attention, since the chapter on the theory of sequence is the stepping stone to analysis in the sense that it teaches the most basic and important tricks and tools in analysis.
0:00 Intro
1:18 Questions and equivalent definition.
11:08 Discovery vs Verification.
12:00 When the terms of the sequence negative/positive
31:45 Vector space of converging sequence
34:18 Product of converging sequence and textbook proof
52:11 Quotient of converging sequence and textbook proof
