Sequences - Increasing, decreasing, bounded and monotonic sequences

In this video we are going to look at increasing, decreasing, bounded and monotonic sequences and a theorem for convergence of a sequence.

[@ConceptualCalculus]

If {an} is monotone and |an| < M for all n then {an} converges--but there is no reason to assume that the limit of {an} is M or even "very close to M" as you say. Consider the sequence an = 1 - (1/n). It is monotonic (increasing) and bounded by 100. That is, for all values of N, |an| < 100. But the limit is 1, not 100.

[@the-Math-guy]

Thank you for your comment but I think you did not understand or hear clearly I never said the limit is M. Also your example of using M=100 is not appropriate it is too far from what one would even intuitively use.

[@ConceptualCalculus]

@@the-Math-guy You said it was M or "very close to M." Listen from 5:25 to 5:35, and again from 8:10 to 8:20. What one intuitively uses is not the point. If M = 100 is a bound then it is a bound, and statements about bounds should apply to it. I am trying to help my students understand the difference between an upper bound and the least upper bound. Similarly, they should know the difference between a lower bound and the greatest lower bound. Now that we're all suddenly teaching online, I'm looking for videos for my students and suggesting the best ones to my colleagues. I"ve watched hundreds of math instructional vids in the last few weeks, yours included. I just noticed that issue and thought a little feedback might be useful. When someone finds an error in one of my vids, I correct it as quickly as I can. Anyway, I did not come here to start a fight. It is your video, and you may leave it that way if you choose.

[@the-Math-guy]

I said it can be M not that it is M. I also called it a "magic value". And it is the case if just like you did, I came to 1 as the value of M, it is an upper bound. My point was to simply show that a condition for possible convergence is a bounded monotonic increasing/decreasing sequence. I never talked about how M is chosen. This is a simple test and all students are already scared of the topic of infinite sequences and series. I did not intend to bring their nightmares back by talking about least upper bounds, infimums, supremums and max lower bounds. As long as they get the point it is sufficient and please check the definitions in most texts they do not dwell on the choice of M, we are talking about infinite sequences as long as there is a bound and its monotonic, it will lead to a convergent sequence. I am more than happy to fix a mistake and have done so before gladly. I still don't agree with you and will leave it as it is. You don't understand the term "magic value" do you? and you believe intuition has no place here, interesting, one of the greatest equations in mathematics is based on intuition. And you did want to pick a fight that's why you made this a public comment and not a private one. Thank you anyway for making me check my video more thoroughly. It also made me spend some time which I had spare. I hope you and yours are safe and well in this difficult time.

[@ArunPrasathh]

Can i know what software u used to write?

[@the-Math-guy]

I used Explain Everything it's an app for tablets

[@gianne9141]

a1...ko ba