Recent content by Paul

Hello everyone! Can anyone tell me a formula (or a way to derive) this integral? \int|f(x)|dx where f(x) is a real, continuous function of x in the vector space C^\infty. So far, all I've figured out is that odd-order integrations are related to the signum function. Thanks!

My thoughts on AP Review Books: Barron's: Most thorough, most serious. Good if you want a really solid review of the subject, but are generally drier than other review books. Nice difficult problems. Don't expect much humour... Princeton Review: Generally significantly less thorough review...

Could someone please suggest a good book for beginning abstract algebra (which would allow me to begin learning number theory)? I've just finished a class in Multivariable Calc. and beginning ordinary differential equations. I will be taking Linear Algebra in the fall. I've heard the name Artin...

What was the error in the proof? They took the paper down...

Thanks, I corrected the typo. And I guess that would put us on the path to a solution. Essentially, given that x is not an element of Z (the integer set), is x^x \in Z possible?

Do you mean the xth root of f(x)? Or am I misunderstanding? And yes, I meant other than simply looking at specific argument and function values.

f(x) = x^x Given this function, defined, let's say for all real numbers, is there any way to tell when x is rational versus irrational for integer values of f(x)? e.g. x^x = 4 x = 2 x^x = 27 x = 3 x^x = 3 x = 1.825455054... Thanks!