Proof of Cayley's Formula: Counting Tree on n Vertices

I discuss a proof of the Cayley's Formula. I take the proof primarily from Prof. Felix Gotti's notes (see references below) and (1) explain the details around arguments stated in the proof, and (2) show examples along the way. Any holes in the arguments presented here are solely due to my lack of ability to be adequately rigorous (this will improve with time!)

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