Group Homomorphisms Map the Identity to the Identity (Proof)

Let G and H be groups and consider a group homomorphism from G into H. We show that f maps the identity in G to the identity in H.

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[ardiris]

The standard high school trig test question is derive the quadratic equation. For some reason, I hit a mental block and I was stumped. Somehow I managed to use 1 * 1 = 1 to complete the square and get the correct answer. Later my teacher said, "You have no idea why this is correct, but you will in six years."

To this day, I have not been able to replicate my exact answer. Close, but not exactly.

[sophiaisabelle]

We appreciate content like this. God bless you always.

[ShaunLovesMaths]

Note that the e_Ge_G is under the operation of G, whereas f(e_G)f(e_G) is under the operation of H.

[paperstars]

Abstract Algebra exam in 3days, Thanks for uploading all those! Do you have videos/recommendations for the sylow theorems?

[Iamrightyouarewrong]

E of G or E'sagee? Like literally what are you saying?