Awesomeness abounds
From a math handout:
What happens if we put a fractional exponent into the formula for the binomial expansion? Or a negative exponent? Needless to say, there is no justification for doing this. It would be like trying to run your automobile on guacamole, or worse, drinking gasoline in the hopes it will make you run faster. The machines were designed for certain fuels and not others. The other formula for binomial expansion was designed and built by a means of successive multiplication by (a + b), a process that yields only whole number exponents.I swear math was not in any way interesting or cool back in high school.
The peculiar thing about putting fraction (and even negative) exponents into the binomial expansion formula, however, is that it seems to work.
posted by NinjaGeek @ 10:15 PM
1 Comments:
The funny thing is, a lot of modern math was developed by doing pretty much this. If you want to completely confuse yourself with crazy realizations, try to take a real analysis or complex analysis course, followed by a good topology course.
Or if you prefer more algebraic things, prove that polynomials of degree 5 or larger don't have a simple solution (like the quadratic formula) with some galois theory.
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