What are Bounded Sequences? | Real Analysis
Support the production of this course by joining Wrath of Math to access all my Real Analysis videos plus lecture notes at the premium tier! / @wrathofmath 🛍 Check out the coolest math clothes in the world: https://mathshion.com/ Real Analysis course: • Real Analysis Real Analysis exercises: • Real Analysis Exercises Get the textbook! https://amzn.to/4lNpyNN Business Inquiries: [email protected] What are bounded sequences? We go over the definition of bounded sequence in today's real analysis video lesson. We'll see examples of sequences that are bounded, and some that are bounded above or bounded below, but not both. We say a sequence is bounded if the set of values it takes on is bounded. In other words, a sequence { An } is bounded iff there exist L, U in R such that L is less than or equal to An is less than or equal to U for all n in N. In other words, every term of { An } is at least as big as L, the lower bound, and no greater than U, the upper bound. If a sequence isn't bounded then it is called unbounded. However, an unbounded sequence may still be bounded either above or below, just not both. Intro to Sequences: • Intro to Sequences | Calculus, Real Analysis Limit of a Sequence: • Definition of the Limit of a Sequence | Re... Sequences that Diverge to Infinity: • Sequences that Diverge to Infinity (Defini... Follow Wrath of Math on... ● Instagram: / wrathofmathedu ● Facebook: / wrathofmath ● Twitter: / wrathofmathedu
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