#math - Mon 5 Mar 2007 between 20:10 and 20:35

NY Lost Funds

 TRWBW emes: yesemes: and x=e^log(x)=sum n=0..inf (log(x))^n/n! zazoru TRWBW, hm yeah... but 332012 could be different ways... like if you chance the first ring with the second you still have 332012 as that... am function you defined TRWBW zazoru: either i'm wrong, the book is wrong, or you are giving the book's question wrong. 3 possibilities. emes so e^sin(0) = sum(n=0...oo) (sin(0))^n/n! ... except sin(0) = 0, and the first term of the series is undefined, 0^0 TRWBW emes: well i kinda grimaced, because i don't like that, but i didn't say anything Olathe 0^0 = 1 TRWBW emes: it's a matter of disagreementemes: defining 0^0=1 is fundamentally a matter of choice, just like any other math definitionemes: 0^0=1 works better for series expansion Olathe Or, you can loosely use the limit style of thinking, and note that with any other value for the power, you always get a 1. TRWBW emes: 0^0 undefined works better in terms of saying a^b is continous for real aemes: if i was writing, i would have written e^x=1+sum i=1..inf x^i/i!, but that's just me emes well, the rest of the terms are zero when x = 0 TRWBW emes: it seems your problem isn't a series question, it's a whether 0^0 is defined questionemes: and like i said, you can do that either way emes well, it is a series question, 0^0 just came up along the way TRWBW emes: if you want, btw, you can define sqrt(9)=-3. i won't stop you.emes: if you want, you can define arcsin(0)=100*pi Olathe Here, you can't define 0^0 as anything other than 1, though, since e^0 = 1. emes how would I go about a second order approximation for the series when the terms are all zero after the first?TRWBW: the range of arcsin is defined TRWBW Olathe: i can define 0^0=cuberoot("apple pie"). but i'll have an uphill climb proving other things. Olathe TRWBW: Sure, but you can't in this problem without contradiction. TRWBW emes: exactly. it is defined. by a person. not by the math king. Olathe The math king will be furious at your dismissal ! emes rex mathematicus TRWBW emes: your teacher might disagree, but truth is he's already bitter because he's teaching high school math. emes lolso to make a second order approximation of e^sin(x) around x=0, I need to take derivatives, correct, because the terms in the series don't cooperate (to bring us back on topic ;) TRWBW emes: not quite. if you define 0^0=1, then the series is like you wrote it. if you don't it's like i wrote it, 1+sin(x)+sin(x)^2/2+... either way, you can make a second order approximation by taking the first terms emes you're right, I was getting caught up by the zerothough that couldn't be considered a polynomial approximation of course TRWBW emes: eh, depends how you define polynomial. ;;) (=double ;) noway- I am having trouble with a proof, http://www.mathbin.net/8714 Steve|Office noway-: So S is both an element and a subset of A? noway- Steve|Office: yes Steve|Office Odd, well, Since S is a subset of A, it is an element of the power set of A. Olathe What does the then mean ? Steve|Office Heh, good question. I parsed it as "and."