by wendy » Fri Aug 01, 2008 8:47 am
It is relatively easy to show that 0^0 = 1, but this can be done without using division. [hint: 0 can be the result of a count].
For division, one should read 0 as 1/u, for a variously large and indefinite u. Some information exists for u in particular instances, so 0/0, as v/u, comes to be definite when there is a definite relation between u and v. Most of the time this is not the case, but there are particular instances where v/u has a definite value. It is this particular instance, that allows Euclidean geometry (where R ~ u), to work, and the relation v/u allows Euclidean geometry to resize without error (ie from R ~ u, to R ~ v).