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Yeah, and I'd be even more interested in a similarly intuitive explanation for the case of complex exponents ;-)
by cousin_it 15y ago
Yeah, and I'd be even more interested in a similarly intuitive explanation for the case of complex exponents ;-)
- baddox 15y agoThat would be difficult, since a formal construction of even the real numbers is a somewhat advanced (3rd or 4th year college mathematics) topic. I forget the details, but I believe a^n for real a and complex n is formally defined using the exponential function (e^x).
- jules 15y agoAt least in the Netherlands, construction of the reals (for example from rational Cauchy sequences) is standard 1st semester stuff. Understanding reals is required or provides a good source of examples for virtually all mathematics courses, so I can't imagine how some universities teach mathematics without it.