Number Theory | Congruence and Equivalence Classes

We prove the congruence modulo n is an equivalence relation on the set of integers and describe the equivalence classes.

[gabrieldoria]

This playlist is awesome!!! I'm a Brazilian student and your lessons are wonderful!!! Congratulations on your didactic.

[georgesadler]

Professor Michael Penn, thank you for another awesome lecture on Congruence and Equivalence Classes in old fashion Number Theory.

[moslemasultana]

very nice venture. Oxygen for us, the noobs attempting to do well in olympiads.

[Thadnill]

Very nice biceps.. the video was also very nice!

[tanjinaaktar]

You can't imagine how much help you do for us❤

[PunmasterSTP]

Congruence? More like con-greatness! Thinks again for making and posting all of these wonderful explanations!

[pariminagalakshmi]

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Once again thank you so much

[Abhisruta]

What textbook for number theory do you prefer?

Good videos...

[dimosvavaitis]

Hi. Thanks a lot! You are doing a grate job! You are helping me a lot to understand Number Theory. May i ask something? At 4:45 at example x=2 and n=3 the equivalence class might have 5 also? {...-4, -1, 2, (5), 8, 11, ...} cause 3|5-2?

[rahelina]

I wish they would replace my prof with you I've been lost this entire week until I found your yt videos

[theunknown]

the sound of the chalk marks striking the board reminds me of old kung fu movies.

[chickensalad]

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[kiddcamel]

when he turns around he looks like mark zuckerburg

[tomnijssen]

Nice video, but why isn't there an equivalence class for n? Why only from 0 to n-1? Thank you! :)

[MicaelSLopes]

não posso dizer que é muito útil...só a transcrição do que qualquer livro de álgebra abstracta diz.

[josephquinto]

I’m a just-graduated senior in high school, but I’m starting to understand this I think 😂