[Date Prev][Date Next][Subject Prev][Subject Next][ Date Index][ Subject Index]

Re: U2-darn few bugs...

On Feb 24, at 12:32 PM, cld@xxxxxxxx wrote:


It's a matter of definition, I think. The negative exponent is
defined to be the reciprocal of the positive exponent. That is, x^
(-n) = 1/(x^n). As to why this definition makes sense, here is one
explanation:

http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Exponents.html

Another reason is that for n>0 and x>0, the function (or set of
functions) y=n^x is continuous (if you graph it for any n, you get
an unbroken line, with the y-axis as an asymptote), which is nice
since y=x is also continuous (an unbroken straight line).

And, of course, once you decide that x^(-1)=1/x you'd better go for
the rest.

But, uhhmm, "unbroken straight line" doesn't really do it for
continuous. I mean, fixing that was why we needed the 19th century....