First of all, any subgroup of index 2 must be normal, so if 2 divides the order of a finite group G and you have an element of order |G|/2, G is not simple.
Secondly, and the *real* point of this post, mathematicians say "let" a lot, as in, "Let x be an element of G." It's entirely possible to read a proof as having a rather bossy tone: "Let x be in G. Don't you DARE not let x be in G. Take H = {e,x,x2,...} - Come on! TAKE IT!! Note that H is cyclic - and if you don't note it, you will be dealt with harshly." I wonder if anyone cowers when they read proofs because the tone interpretation section of their brain is a little bit broken.
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3 comments:
Um, yes. 2 + 2 = 4.
Laverna, there's more to this. Spencer looked at my license plate and laughed because "UDU" apparently is comical to math nerds. He explained it, and the sad thing is, I understood the words, but as a whole...I got nothin.
Please do not advertise your true nerdiness (cool word)!
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