Proof: Cosets Partition the Group | Abstract Algebra

[@TheWildStatistician]

Hey don't be discouraged if you are not getting as many views as you'd liked because I'm sure that one day with this quality of content, you will surely grow! Keep attacking relentlessly at your goal and you will get there my guy :)

[@SaiyaraLBS]

YESS! I came here to tell him this as well! Let him know he should keep doing this and we are very grateful for that!

[@WrathofMath]

I feel obliged to shout out one of my all-time favorite books, A Book of Abstract Algebra by Charles Pinter, which plays a significant role in my presentation of these topics. Affiliate link: amzn.to/3IjoZaO

[@punditgi]

The Wrath returns! Excellent! 😃

[@WrathofMath]

Thank you, Ezra! Almost to Lagrange's theorem!

[@SaiyaraLBS]

@@WrathofMath please keep making more content you’re an amazing teacher you’re helping so many viewers immensely and creating great content to last forever!

[@hoaang6839]

Hello, just found your videos and I really appreciate them! Your explanation is clear and structured. Subscribed!

[@WrathofMath]

Thank you! I'm trying to make these the best Abstract Algebra lessons available. Still a long ways to go to finish the playlist, but let me know if you have any topics you'd like covered sooner than later!

[@SaiyaraLBS]

Hi !! Love your content, please keep it up. Especially your series on Graph Theory helped me a lot! Speaking of that, I would like to request a proof in Graph Theory as well : “every planar graph can be expressed as a union of five edge-disjoint forests”. Thanks!

[@WrathofMath]

Thanks Nøshin! I'm looking forward to getting back to the Graph Theory playlist when I have time. I'll see what I can do about that proof, thanks for the request!

[@SaiyaraLBS]

@@WrathofMath thank you!! I have discrete math exam in an hour including graph theory haha thanks to you I feel confident!

[@BeatrizSilva-qt7fn]

You explain very well, thank you

[@WrathofMath]

Glad it was helpful!

[@bangvu2127]

Many thanks

[@WrathofMath]

Thanks for watching!

[@erinmeyers-t9w]

Great proof

[@Sarah-pu8un]

Extremely helpful. Thanks!

[@WrathofMath]

Thank you for watching, glad to help!

[@golden_smaug]

Hi, I have a question. In the proof that every element of G is in some Ha, couldn't the statement ec=c∈Hc imply that e∈Ha for all a∈G ? I mean, I'm convinced by the other video that e∈Ha for one single coset, but this last proof gave me that idea and now I'm a bit confused 🙁

[@danielc36]

A bit late but no! ec=c ∈Hc does not imply e ∈Ha for all a∈G. Could you clarify how you got ec∈Hc ---> e∈Ha ∀a∈G?

[@ssh2791]

Thank you very much! I love your videos. They really help me a lot. Can you please make disecrete math playlist with new videos and already existing vids by ascending difficulty.

[@WrathofMath]

So glad to hear it, thank you! I have a Discrete Math playlist, but it is currently unlisted because it is very small (don't want to take up space in my playlist list for such a small playlist): kzbin.info/aero/PLztBpqftvzxXgpx57CEhZScNk2lWs1LdU There are several lessons I have which could conceivably be put in the playlist, but I might just make new versions of those videos that are a bit more targeted towards a Discrete Math audience. Of course, many of my graph theory videos could also go in the discrete math playlist, but I go into depth with graphs past the point required for an average discrete math playlist, so the graph videos stay on their own. Let me know if you have any lesson requests for the discrete math playlist! Currently I am more focused on abstract algebra and real analysis, but I'm happy to jump over to discrete for a lesson or two.

[@SimchaWaldman]

02:43 Why can't one just say that if x ∈ (Ha ∩ Hb) then x ∈ Ha and x ∈ Hb, and therefore Hx = Ha = Hb?