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I very strongly object to this convention, as both a programmer and a mathematician. A basic theorem is that for any field we must have that a/b = c/d if, and
by calhoun137 8y ago
I very strongly object to this convention, as both a programmer and a mathematician.
A basic theorem is that for any field we must have that a/b = c/d if, and only if, ad = bc. See theorem 2 in this classic text here for a proof[1]
So if 1/0 = 0, then we also have 1/0 = 0/1, which implies 1 x 1 = 0 x 0 which is a contradiction. But then we also have 1/0 = 0/x for any x, hence we also have shown x=0 for any x, which is an infinite number of contradictions. Is this a problem which is addressed in the post that I missed?
By the way, I have spent more time than it's polite to discuss in public studying the topic of dividing by zero, and also what 0/0 means. If you are also interested in this topic, the best youtube video is by Mathologer and I highly recommend it to everyone. See here [2]
[1] https://books.google.com/books?id=3ApEDwAAQBAJ&lpg=PP1&pg=PA4#v=onepage&q&f=false https://books.google.com/books?id=3ApEDwAAQBAJ&lpg=PP1&pg=PA...
[2] https://www.youtube.com/watch?v=oc0M1o8tuPo https://www.youtube.com/watch?v=oc0M1o8tuPo