What are Monotone Sequences? | Real Analysis

We introduce monotone sequences, monotone increasing, and monotone decreasing sequences, with plenty of examples and non-examples. We'll see how a sequence can be both increasing and decreasing, and we'll see some equivalent characterizations of increasing and decreasing sequences. #RealAnalysis

We'll also discuss what it means for a sequence to be strictly increasing and strictly decreasing, and what it means to be eventually increasing and eventually decreasing.

★DONATE★

Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon!

Follow Wrath of Math on...

[WrathofMath]

Check out my proof of the monotone convergence theorem, and a fun example using it!

[nooradleena]

love it when the videos can make it more simple!

[Zinani-zb]

Very nicely clearly explained. Thank you very much ❤️🌹

[enzokuhlemsotra]

thank you very much sir you explained very well

[sheharayar]

Avid follower of your videos! Keep up the great work 👌👌. I couldn't help but notice a detail. At the 11:28 timestamp, you illustrate an increasing function, stating that Am is greater than or equal to An when m is greater than or equal to n. However, when addressing the scenario of a decreasing function, you mention that An is greater than or equal to Am under the condition that (Am is greater than or equal to An). Could this be a typo? From my understanding, in this case, Am should be less than or equal to An. Thanks for clarifying.

[donitarose]

Thank you so much for this video, prof!
Note: I am confused at 11:45-11:55, why is m >=n, and not m <= n? Isn't it for a monotone decreasing sequence, the terms will be decreasing? So, m terms are decreasing as you go through sequence, ie. m <=n?

[mjeghss]

(A monotonic increasing sequence is convergent if and only if it is bounded.)

[krasimirronkov]

Is there a theorem that states that if the limit as n tends to infinity of the sequence a_n+1/a_n is between 0 and 1 then the limit of a_n is equal to 0

[sefakorhonorinedossou]

Sir please can you help us with examples and explanations of balls