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@sbagley Honestly that might have been the most fun I had prepping for abstract algebra last spring when I realized that (a) it wasn't an axiom and (b) the book never explicitly asserted it. "Oh gosh have I been making an undue assumption this whole time?!"On twitter.com
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@sbagley Anyway it'll bug me unless I finish it without assuming 0x=0. (-1)x = (-1)x + 0 = (-1)x + x + (-x) = (-1)x + (1)x + (-x) = (-1+1)x + (-x) = (0)x + (-x) = (0)x + (0)x - (0)x + (-x) = (0+0)x - (0)x + (-x) = (0)x - (0)x + (-x) = -xPermalink On twitter.com