Monotone convergence from the supremum principle

This video visually demonstrates the proof that a monotone increasing sequence bounded above converges to its supremum. Using an animated coordinate system, it plots a rising dotted curve representing the sequence {a_n}. It introduces the least upper bound L and an arbitrary value L - ε. By leveraging the properties of the supremum and the sequence's monotonicity, it establishes that for sufficiently large n, the terms are trapped within the interval (L - ε, L], thereby proving convergence.

Before you watch

• Epsilon-N definition of limits
• Properties of ordered fields