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Aunc.1961 net.math utcsrgv!utzoo!decvax!duke!unc!bts Sat Mar 13 20:28:32 1982 log(0) revisited There is a problem with the argument that log 0 - log 0 = 0, unfortunately. It is just as easy to take limits as follows:

Lim log(a) - Lim log(b) = a -> 0 b -> 0 ???

There are many cases where you'll get into trouble if you assume that two variables are going to 0 at the same rate. As far as ways to deal with log of 0, I rather like infinitesimals. Replace the 0's with a and b, where a and b are "infinitely close" to 0. Then the algebra works, but you won't necessarily get 0 or even another infinitesimal as the answer. Adding a single point at infinity looks nice topologically, but you get into trouble using that point algebraically; it won't obey the same rules as "finite" points. A good source for non-standard analysis is the first few chapters of Stroyan and Luxemburg's text. (Oh yes, if you replace both occurrences of 0 with the same infinitesimal, you do get 0.)

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