Real Analysis | Sequences and the ε-N definition of convergence.

We present the ε-N definition of convergence for a sequence and give a few basic examples.

Books I like:

Abstract Algebra:

Differential Forms:

Number Theory:

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[drpkmath]

Pretty sure Michael has many threads ready. I am preparing for a full one year advanced undergrad real analysis video series as well. Ring theory would be interesting topic for making couple of separate videos for sure!

[ashrayne]

You've just cleared up week 1 of Real Analysis in 8 minutes, thank you.

[matrixmash]

Thank you so much for the real analysis playlist. This is immensely helpful, a lot of my classmates and I are struggling to understand the concepts fully as our textbook essentially blows through the definitions and propositions like their either the most trivial results or, for "brevity", leaves a lot of the back-end material out. Definitely shared this playlist.

[sarojpandeya]

Thank you for starting mathematical analysis.

[superorangebody]

Dude this is so good. I'm reviewing for a final exam in my intro to analysis class and your videos really help!

[cloriscloris]

Omg, this is so clear！I wish u were my professor.Thx for saving my midterm, Sir.

[noahtaul]

Wow, how many threads do you have going on at once? Sequences, group representations, differential topology, contest problems, maybe ring theory...

[gilbertchan]

thank you, you've single handedly saved me from my real analysis subject

[languageoflogic]

Most proofs I’ve seen start with “let’s assume..“, but math is a science requiring facts to be focused on to avoid assumptions. This guy starts with “given” and he goes through the proper steps. Subscribed.

[valeriereid]

Very well explained. Thanks for your contribution to mathematics education.

[AilinZeng-st]

wow this is amazingly clear thank you so much. my professor doesn't really explain anything i always get so confused listening to his classes

[FabianAguilar-uv]

Thank you. This was a great review before my class.

[chaoticlife]

@michael penn I'm using your videos to review my real analysis course. I wish in my course, they mentioned you choose the value of N in your "scratch work". It was so hard for me to wrap my head around that idea. At the time it felt like going on a loop and doing the proof twice.

[ayeshasiddiqua]

Really found helpful...now I literally understood the concept... thankyou!

[claireelizabeth]

So happy for some real analysis content! Discussion of Riemann-integrable functions would be much appreciated if you were into suggestions.

[abhijitharakali]

Mystery of dislikes continues! I witness many videos of superb quality, getting dislikes. What's the deal with you people? Mike is doing a favor for strangers by providing short tutorials on useful material. At least, abstain from watching any of his videos if you, for some mysterious reasons, not like the content. Why watch the video and hit the dislike button?

[mimodite]

Maybe this is semantics but isnt it wrong to say that the "band" (strip which is epsilon distance from L) gets smaller when n gets larger? Isnt it other way around? In the sense that if we take smaller epsilon, n that is sufficiently big probably gets larger?

[TheSpark]

I love your videos! Keep it up! You are saving lives :D

[ayoubnouni]

Or you can take N =[1/sqrt(epsilon)]+1
[***] means the floor function

[duckymomo]

are you gonna do topology? (open sets, etc)