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This is just a proposition in my book with a proof following it. What I don't get is the very beginning of the proof: "Let ##|x| = n##. The elements ##1,x,x^2,\dots, x^{n-1}## are all distinct elements because..."

Isn't the fact that ##|x| = n## part of what we wanted to prove? Why does the proof just "let" this be the case?