Quote:
Originally Posted by Nereid
If I recall correctly, there's also some neat stuff on limits, so that in some cases what 'looks like' 0/0 (for example) - in the limit - is well defined. In (at least some of) these cases 'division by 0' may 'make sense'.
More generally, 'math' is a formal system, so why certain things 'make sense' and others don't is entirely determined by the axioms of the piece of math you are working with.
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Yes, but all of the mathematics that most people have ever seen, including most physicists is based on the basic axioms that permit ordinary arithmetic. That is the Zermelo Fraenkel plus choice system, or what is often seen as the Peano Axioms.
http://en.wikipedia.org/wiki/Zermelo...kel_set_theory
They do not permit division by zero under any circumstances.
It is possible to talk about things like Y/X and take limits in a meanigful way in some circumstances in which the limits of Y and X separately tend to zero. That is case for instance with (sin x)/x which tends to 1 as x tends to 0, but that is not division by zero. You probably dealt with this one using L'Hopital's rule in an introductory calculus class.
Mathematics is just not that arbtrary.