Some important facts about ≡ (mod n)

We prove some important facts about a very important equivalence relation on the integers -- congruence modulo n.

If you are going to use an ad-blocker, considering using brave and tipping me BAT!

Books I like:

Abstract Algebra:

Differential Forms:

Number Theory:

Analysis:

Calculus:

My Filming Equipment:

[goodplacetostop]

20:16 Homework: pause the video and fill in the blanks
24:35 Good Place To Stop

[tomctutor]

@22:35 Ok Michael has convinced me that 4=0, 3=0, 2=0 etc so ∀N=0 and all integers add up to nothing. I think I understand Equivalences now!

[oskaradolfson]

Where can I find a collection of the proof-writing videos?

[echandler]

Very nice video. I wish you had talked more about the utility of equivalence classes in reduction, for example negative residues.

[math]

watching and learning bro, here for the challenge, very well explained, the rest I can easily do

[davidcroft]

Dear Micheal, can you solve this differential equation: df/dx=f*g(x)/(f^2-A^2), where f(x) is a function from R+ to R+, A is a constant and g(x) is a function only of x (such as 1/x, 1/x^2, etc.)?
Thank you in advande for the response and the video.
P.S.: your channel is great, in the last month I really fell in love with your video and fantastic math trick!

[criskity]

For some reason I have a tendency to call the ≡ sign "threequals".

[fakhermokadem]

hope this is followed by a vid on quotient space

[yoav]

Isn't it related to abstract algebra ?

[mathsandsciencechannel]

wait, wait, wait, wait!!! You cant miss the maths and science tutorials, hurry and check it out student. thanks