What are Bounded Sequences? | Real Analysis

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.

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[punditgi]

Lucky for us your enthusiasm for teaching math is unbounded! 😊

[debarthasaikia]

Man are you the real santa because you gave a good lesson for learning bounded sequence as a present ❤❤🎉🎉

[ChocolateMilkCultLeader]

Your accent is amazing. I could listen to your voice for hours

[nenanena]

Please we need topology videos your explanation is perfect

[omerayman]

C is the maximum of absolute values for both L, U

[adoxographer]

Worth subscribing for the Christmas sweater alone.

[mahmoudalbahar]

Many thanks for this good when it is convenient to you continue with this real analysis course and examples about it....and if it is possible please make videos about number theory.

[yukipaisen]

Who knew a man in a Christmas sweater would help me with my math class lmao

[nurainnadiahbintibaharudin]

Thanks a lot for your video :) keep spreading the beauty of math.

[tomnijssen]

Why is the upperbound not "1" in the first example? 1/n takes on al values between (0 and 1) for n in N. :)