zaphod

i understand now. (or at least i think i do haha). thank you. i'm about halfway done with my BSc. all of my linear algebra and calculus is done, but i havent taken any abstract algebra or number theory yet other than the bits that i've read and done on my own. so, not really no.

another question about method 1, if you please: do you have an example where the base a is not 10?

could you give a numerical example that demonstrates this theorem, please? i just want to be sure that i understand it.

herme3, get a clue

were you able to invent something over the weekend, johnny?

did you not read his post at all?

thats not something that has been confirmed by anyone. if anything i would expect george lucas to address this eventually and deny this connection. it is AT BEST left to interpretation, but there is no reason for anakin's mother, a slave woman on tatooine, to be the product of some sith experiment.

i'm sure you will. you always do.

well, i know you're gonna hate this explanation, but the Gamma function is defined as [math]\[\Gamma(x) = \int_0^{\infty} t^{x-1} e^{-t} \,dt\][/math] for x > 0. although, the exact proof that you're looking for, which is a simple expansion on this definition can be found here: http://mathworld.wolfram.com/GammaFunction.html i'm just honestly too lazy to redo the LaTeX to make it clear. just scroll a little down the page right under those pretty little colored graphs. there lies your answer. if you need any furthur proofs of why this and that, you can email wolfram.

no. it is not. the limits at z=1 are equal to 2' date=' but that says nothing about the value of f(z) when z=1. [math'] f(z) = \frac{z^2-1}{z-1} [/math] is not the same function as [math] f(z) = (z+1) [/math] yes, seem very similar when you graph them out. but one is defined at z=1 and the other is not. stop trying to re-define shit, johnny. you're not going anywhere with this bullshit.

to be fair, so is the number of atoms in the universe.

i dont know if someone has already mentioned this, but after these threads about "what is this-or-that, intuitively?", here is the FINAL ANSWER to life, the universe, and everything: it doesnt matter. mathematics is not about intuition. at all. end of thread.

[math]\[n! = \int_0^{\infty} x^n e^{-x} \,dx\] [/math] check for n = 1 [math]\[\int_0^{\infty} x^1 e^{-x} \,dx\ = 1\] \[\ 1 = 1!\][/math] check for n = (k+1) [math]\[\int_0^{\infty} x^{k+1} e^{-x} \,dx\ = \Gamma(k+2)\] \[\Gamma(k+2) = (k+1)!\][/math] yada yada yada, QED

rather easy

some people try to think too much. a negative number, intuitively, is a negative number.

see sig

weird.. i learned it as BEDMAS in high school Brackets, Exponents, Division, Multiplication, Addition, Subtraction

but the fact of the matter is that there are no contradictions involved.

if thats the case, then irrational numbers (and hence real numbers) were invented from the "desire" to have a solution to sqrt(2). and i guess natural numbers were invented from the "desire" to have a solution to the question: "how many apples in basket, mr caveman?" whether or not you think you've discovered something about the nature of mathematics, the fact of the matter is, you havent. complex numbers are a valid (and useful, to boot) number system.