Definition of the Limit of a Sequence | Real Analysis

What are convergent sequences, and what is the definition of the limit of a sequence? We introduce the definitions, with examples and a proof in today's video lesson!

In the definition of the limit of a sequence, we seek to capture what it means for a sequence to get arbitrarily close, or converge, to some limiting value. We do this by using an arbitrarily small "tolerance" value called epsilon. If you're in an analysis class, get ready to write "Let epsilon be greater than 0" an awful lot.

I hope you find this video helpful, and be sure to ask any questions down in the comments!
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[nihilisticboi]

The moment you finished explaining the 1/100 example, I felt I reached enlightenment. Beautifully explained!

[hamadkhan]

Sir, this is the best lecture of this topic on u tube. Thank u so so much for explaining everything. This was hard to me but u explained it in a very easy way. why so underrated? You are really good, I hope that soon you will have subs in millions🙏🙌

[pxlbits]

I learned more in this video than my entire semester in analysis class lmao...

[stephen]

These intro to analysis videos are incredibly valuable. You have clarified the ‘setting out’ stage of the proof that my textbook simply failed to describe. How to choose an N? Thanks to your teachings, I can understand analysis and apply its techniques! I had thought that perhaps I had truly arrived at a level of maths which I’d find incomprehensible (at least without some miraculous discovery), but your teachings elucidated the simple technique of how to algebraically decide what N ought to be. So thank you so much! This will certainly be the most valuable lesson in analysis of my life! Such is the nature of this incredible inflection point!

[manarmagdy]

I cryied because I couldn't understand that and my exam after 4 days but now it's more than clear. Really thanks from my heart

[swastikadeb]

I was really struggling to understand the definition of limit clearly. I looked up everywhere on the internet until I found this video, such nicely explained with that amazing 1/100 example. It's totally clear now! Thank you sir. Hope this reaches to everyone out there.

[bigollameo]

Now I finally understand what the "n>N" condition means. For the longest time I've been puzzled as to just what this relation requirement was trying to communicate. Should have been apparent years ago, but better late than never.

Thank you!

[nikeshlilani]

this is by far the best lecture on this topic on youtube..thanks a lot sir !

[natemanify]

My professor just went over this topic and I just could not follow along or understand what he was trying to say. But this actually makes sense, because of you im actually completing my homework. Thank you!

[DoEvenly]

this video is the best video about limit I have seen in this year 😮

[ConstanceShayamano-eifc]

Yu the best online teacher I have ever encountered with

[AmeenaMuddasir]

Ahh great sir ! I was focusing on what is actually written in the book but got really upset because I was wasting my own time ! Then it clicked in my mind Ka I should watch a video and luckily I got you and your video ! Very good job sir thank you ❤

[IdoYos]

Best explanation I have found so far!! If you could make videos explaining linear algebra as well it would be phenomenal!! Thank you so much!!

[le_great_escape]

I finally understand where my professor for 1/epsilon. THANK YOU!

[bactran]

amazing explanation of the limit of sequence definition that blows my mind. Thanks a lot Wrath. Please keep doing your great works

[Anonymous-rvgz]

Man you saved my 48hrs of
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[liss]

perfectly explained, well defined that makes things clearer than on the mere printed definition from the book.. Thanks for this tutorial video it really helps a lot.. 👏👏👏

[samaritan]

Math 101 in Uni and you make it sound so simple. I like the style

[aqsamaryam]

I think it is the best explanation for anyone to understand this