What are Monotone Sequences? | Real Analysis

[@WrathofMath]

Check out my proof of the monotone convergence theorem, and a fun example using it!
Proof of Monotone Convergence Theorem: ua-cam.com/video/4NURDmE79VU/v-deo.html
Fun Example of Monotone Convergence Theorem: ua-cam.com/video/AuvBS7UKxqU/v-deo.html

[@nooradleena]

love it when the videos can make it more simple!

[@WrathofMath]

Thanks for watching, Noor, I am glad it helped! If you're looking for more analysis, check out my playlist!
ua-cam.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html

[@Eis461]

More Real Analysis Videos please

[@ian.ambrose]

Thank you, Professor.

[@WrathofMath]

My pleasure! Let me know if you have any questions, and check out my analysis playlist for more! ua-cam.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html

[@Zinani-z7b]

Very nicely clearly explained. Thank you very much ❤️🌹

[@WrathofMath]

Glad to help - thank you for watching!

[@enzokuhlemsotra6383]

thank you very much sir you explained very well

[@WrathofMath]

Thank you - glad to help! Let me know if you ever have any questions!

[@Eis461]

We need more Real Analysis videos

[@WrathofMath]

That we do, I work as fast as I can, the the real analysis videos take a lot of care to complete. Let me know if you have any specific requests for what topics you want covered next. My current list has me proceeding through the topology of the real numbers, though I will have to skip the Heine-Borel theorem until I have a more open schedule with time to do a lesson on its proof.

[@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.

[@WrathofMath]

Thank you! I double checked my explanation and it looks correct to me. I don't know if you had a typo in your question or if you just misheard me, but it doesn't look like you typed what I said. When addressing decreasing sequences I said an is >= am whenever m>=n. So if a term comes later (m>=n) then it must be less than or equal to the preceding terms.

[@donitarose4353]

Thank you so much for this video, prof!
Note: I am confused at 11:45-11:55, why is m >=n, and not m

[@meghnachaudhury8013]

it is m>=n because the values keep decreasing as we go further. For example, in a sequence like (1/n)= (1,1/2,1/3,...), the values keep on decreasing. Here a1=1, a2=1/2 where 2>=1 but a1>=a2, that is an>=am but m>=n

[@yuanfeng4194]

Ty for the help

[@user-mj8eg1hs1s]

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

[@aashsyed1277]

Thanks so much!!!!!

[@krasimirronkov17]

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

[@hovaiho8690]

Thank you so much 😊

[@WrathofMath]

My pleasure - thanks for watching! Let me know if you have any lesson requests, and if you're looking for more analysis, check out my playlist! ua-cam.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html

[@derickmweembela4248]

Exam in Two week's 😢

[@WrathofMath]

Good luck!

[@sefakorhonorinedossou5709]

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

[@samwelgithuo6108]

Educative

[@alessandrorossi1294]

First!

[@WrathofMath]

Thanks for watching!

[@leomessigoalsonly8102]

Thank you so much ❤️

[@WrathofMath]

My pleasure, thanks for watching! Check out my analysis playlist if you're looking for more, and let me know if you have any questions!
ua-cam.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html