At 0:45, I think you meant S={a,b,m,n in Z | am+bn} instead of defining the set with two a terms.

Great video: really good explanations and aesthetics! On a side note, in my abstract algebra class, they proved r had to equal zero another way: their proof included the assumption that a and b cannot equal zero and am+bn>0, and because r is an element of s and r

From excursion

Greatttt