Proof: Cancellation Law for Groups | Abstract Algebra

We prove the cancellation law for group elements. If we have three elements, a, b, and c, from a group G, and we know ab = ac, or ba = ca, then we can conclude that b=c. In other words, we can cancel the a's on the left, or cancel the a's on the right, just like we always have in algebra! The proof is nice and painless. Note that if ab = ca, we cannot cancel the a's because they are on different sides. However, if G is commutative, we could write ab = ca = ac, then cancel the a's on the left to have b=c.

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[zethayn]

This has got to be my favourite proof ever, thank you!:D

[nonentity]

I miss these types of video, even though modern ones are better in terms of quality.

[shoopinc]

Thanks wrathofmath for bringing us math from the most dangerous warzones.

[ricksun]

Great presentation! Just found out your channel. Good work!🥳🥳

[davidshi]

A surprising one is the inverse of a product, which leads nicely to the definition of commutator subgroups.