The monotone sequence theorem states that every bounded monotonic sequence of real numbers converges. More precisely, an increasing sequence which is bounded above converges to its supremum, while a decreasing sequence which is bounded below converges to its infimum.
Monotone Sequence Theorem
See also
Bounded Sequence, Infimum, Monotonic Sequence, SupremumExplore with Wolfram|Alpha
References
Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.Referenced on Wolfram|Alpha
Monotone Sequence TheoremCite this as:
Weisstein, Eric W. "Monotone Sequence Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MonotoneSequenceTheorem.html