Algebra 6 | Cancellation Property

[@StratosFair]

I enjoyed the proof of the main result :)

[@YouTube_username_not_found]

I think the video should have also defined this property Divisibility: a is right-divisible by b if there exist x such that a = xb a is left-divisible by b if there exist y such that a = by What should be retained from the video: in a semigroup, divisibility is enough to prove that G is a group. However, cancellability is not enough unless the semigroup is finite because in that case cancellability and divisibility are equivalent. What I found interesting is the fact that f_a and f_b, when they both correspond to an associative binary operation, and are surjective, then they are injective and thus bijective. In similar words, divisibility implies cancellability.

[@brightsideofmaths]

Also a good approach!

[@YouTube_username_not_found]

@@brightsideofmaths I just restated what's in the video, I don't think I have came up with something new 😅 .

[@brightsideofmaths]

@@KZbin_username_not_found I like the approach with divisibility.