I would say that division is an operation restricted to a non-zero second argument. As such, asking for a boolean answer to "does zero divide x" is nonsense, with neither a "true" nor a "false" result. Even when x is zero. Maybe it's like asking if the square root of -2 is even. On Wed, Feb 11, 2015 at 3:51 PM, James Propp <jamespropp@gmail.com> wrote:
Mathematica refuses to answer the question, and I've seen textbooks that duck the issue as well ("Suppose *a* and *b* are integers, with *a* nonzero. We say *a* divides *b* if and only if ...").
In fact, Mathematica also refuses to answer the question "Does 0 divide 1?"
Is it a standard convention that *a*-divides-*b* is a relation on (*Z*\{0}) x *Z*, so that asking whether 0 divides 1 is no more sensible than asking whether pi divides the square root of 2?
I would've been naively inclined to the view that 0 divides 0 is TRUE, while 0 divides 1 is FALSE.
I'm afraid to post this question to MathOverflow, lest I be reprimanded for asking such an inappropriate question ("Is this a homework problem that your professor assigned you?"). You guys are nicer, and more to the point, you all know me.
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