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

NY Lost Funds



TRWBWemes: yes
emes: and x=e^log(x)=sum n=0..inf (log(x))^n/n!
zazoruTRWBW, 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
TRWBWzazoru: either i'm wrong, the book is wrong, or you are giving the book's question wrong. 3 possibilities.
emesso 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
TRWBWemes: well i kinda grimaced, because i don't like that, but i didn't say anything
Olathe0^0 = 1
TRWBWemes: it's a matter of disagreement
emes: defining 0^0=1 is fundamentally a matter of choice, just like any other math definition
emes: 0^0=1 works better for series expansion
OlatheOr, you can loosely use the limit style of thinking, and note that with any other value for the power, you always get a 1.
TRWBWemes: 0^0 undefined works better in terms of saying a^b is continous for real a
emes: if i was writing, i would have written e^x=1+sum i=1..inf x^i/i!, but that's just me
emeswell, the rest of the terms are zero when x = 0
TRWBWemes: it seems your problem isn't a series question, it's a whether 0^0 is defined question
emes: and like i said, you can do that either way
emeswell, it is a series question, 0^0 just came up along the way
TRWBWemes: 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
OlatheHere, you can't define 0^0 as anything other than 1, though, since e^0 = 1.
emeshow 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
TRWBWOlathe: i can define 0^0=cuberoot("apple pie"). but i'll have an uphill climb proving other things.
OlatheTRWBW: Sure, but you can't in this problem without contradiction.
TRWBWemes: exactly. it is defined. by a person. not by the math king.
OlatheThe math king will be furious at your dismissal !
emesrex mathematicus
TRWBWemes: your teacher might disagree, but truth is he's already bitter because he's teaching high school math.
emeslol
so 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 ;)
TRWBWemes: 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
emesyou're right, I was getting caught up by the zero
though that couldn't be considered a polynomial approximation of course
TRWBWemes: eh, depends how you define polynomial. ;;) (=double ;)
noway-I am having trouble with a proof, http://www.mathbin.net/8714
Steve|Officenoway-: So S is both an element and a subset of A?
noway-Steve|Office: yes
Steve|OfficeOdd, well, Since S is a subset of A, it is an element of the power set of A.
OlatheWhat does the then mean ?
Steve|OfficeHeh, good question. I parsed it as "and."

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