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#1251 Re: Help Me ! » ... equation ... » 2006-06-01 01:34:36
NO SOLUTION Because X in the equation do not have a defination on 0.
But you can just put a very large number (positive or negative) as a "solution".
When X is very large, the difference between 3/X and 4/X is very small, hence neglactable in some sense.
Praticly, think of a pair double stars from far far away, does the gravity from the two make any difference for you?
Still, I will not say the answer is infinity, since it is my belief to deny a single nonvariable infinity.
#1252 Re: Help Me ! » Differential Equation » 2006-05-30 03:27:00
COMPLEX FUNCTION????
#1253 Re: Help Me ! » Proving Linear Algebra » 2006-05-30 03:23:37
The key is to prove the two definations of dot product are equivalent.
Def1: dot product is the sum of corresponding cartesian co-ordinates.
Def2: dot product is the product of two vector lenths, and the cosine of their angle.
Usually this is proved within a triangle consisting of vector OA, OB, and AB=OB-OA
In a catesian system, distance formula is true based on Pythagoras' Theorem.
So if you define A(x[sub]1[/sub],y[sub]1[/sub],z[sub]1[/sub]) B(x[sub]2[/sub] ,y[sub]2[/sub],z[sub]2[/sub]), you get
meanwhile, Cosine Theorem
then below must be valid
proven 
#1254 Re: Dark Discussions at Cafe Infinity » Preparing » 2006-05-29 23:11:43
I don't prepare. Come what may.
#1255 Re: Dark Discussions at Cafe Infinity » do you procrationate? » 2006-05-29 23:10:04
I tidy my room usually when I have to-otherwise I won't find my stuff.
#1256 Re: This is Cool » 2-D or 1-D jumble » 2006-05-29 23:07:01
Not possible.
2 lines may determine a plane, whether being verticle or not.
But a plane can never be determined by 1 line. Because it's more complex by one dimension.
#1257 Re: Dark Discussions at Cafe Infinity » do you procrationate? » 2006-05-29 03:46:42
I postpone things less important.
#1258 Re: Help Me ! » reciprocals » 2006-05-28 00:42:52
2 and -3
#1259 Re: Help Me ! » Sum of an Infinite Series » 2006-05-27 22:42:26
thanks a lot!
#1260 Re: Help Me ! » Differential Equation » 2006-05-27 22:01:14
It's amazing to see someone solving a DE with a "y''" so easily.
#1261 Re: Help Me ! » logarithmic coordinates » 2006-05-27 14:24:22
Think the y axis to be fake, it displays some loga10 loga5 instead of 10 and 5, so same distance means multiplied by same value.
#1262 Re: This is Cool » Cool Perfect Power Function!!! » 2006-05-22 23:15:14
Since p is a prime number, how can it divide i?
#1263 Re: Help Me ! » trigonometry » 2006-05-22 03:20:03
you can use imageshack and (img)http://.......jpg(/img) "(" and ")" should be "[" and "]" instead.
#1264 Re: Help Me ! » p-value and CIs » 2006-05-22 03:11:34
statistically significant means initially you assume the expectation 0, then check probability of the value and values further (from 0), double it to get p value, and p value is less than 0.05.
a suspicious very small p value means statiscally signifcant, which means you have a nice confidence to say the 0 assumption wrong, or statiscally rejected.
Today is Sir Arthur Conan Doyle's birthday, so I would take his geneous detective for example. As Sherlock Holmes had got his bunch of evidences, the suspect could had the chance to be innocent, and the evidences could had been pure coincidences, but the probability was so low that the innocence assumption should be rejected.
However, his p value could be far less than 0.05, I think. And it's very responsible for a statician to not only say the signifancant conclusion but also give out the p value for others to judge.
#1265 Re: Help Me ! » Sum of an Infinite Series » 2006-05-22 02:28:11
Thank you liuv, good shifting! My thought is
for krassi holmz,
you may check out some properties for prime numbers.
PS> how did you put "n->∞" under "lim"?
#1266 Re: Dark Discussions at Cafe Infinity » do fish have a personality » 2006-05-20 21:29:51
A fish is very smart. If you have ever tried to fish a fish, you would know it's really a difficult thing to fool a fish and really an easy thing to feed it against your will.
#1267 Re: Help Me ! » Sum of an Infinite Series » 2006-05-20 21:08:57
How do you transform it into a Rieman Sum? There is no Δx or another 1/n in it!
The integral is indeed a limit if you admit the property of Delta Function:
where
#1268 Re: Help Me ! » Sum of an Infinite Series » 2006-05-19 03:22:17
Yes, and that does return a limit result log2 
#1269 Re: Help Me ! » Bart Simpson Rocks » 2006-05-19 03:09:14
Math can get you lots of money when you grow up. Bart Simpson can't.
???????How???????
#1270 Re: Dark Discussions at Cafe Infinity » imballanced brain... » 2006-05-15 02:50:58
Find a math book you understand and pour a bottle of glue onto your chair , sit(makes sense now), then start reading and practicing.
My initiative is like yours. But soon I found that there's not a "quick" way to cover math.
A psycologist studying creativity found that until there're enough "poles" in one's brain, advanced web for creative thinking could not form.
So you should get some comprehensive books and some interesting books, and go to our forum often- to set those "poles".
#1271 Re: Help Me ! » Lagrange » 2006-05-15 02:37:32
you can set up a distance function,
maximize it or its square under the constraint z=4-x^2-y^2.
#1272 Re: Help Me ! » Sum of an Infinite Series » 2006-05-15 02:33:51
Good.
The interesting here is that n is in non-trivial place in the sum.
Yes, you are smart!
To Zmurf and Krassi:
Originally it's a Rieman Sum, an integration question. So I guess Krassi has used integral.
Original Question:
#1273 Re: Dark Discussions at Cafe Infinity » The philosophical ramblings of a skitzo. » 2006-05-14 18:30:00
Why did I say insufficient? You cannot have 2 same apples, so 2,3...are just approximations for reality.
However, they are the same based on how we judge "sameness." For a mathimatical example, 2 is certainly not the same as 4, but if we judge them based on mod 2 (the remainder when they are divided by 2), then they are the same.
In the same way, the two apples are not exactly the same like 2 and 4, but we call an apple that because it is fruit that comes from an apple tree, and thus, they are the same by how we judge them.
Sorry for my rude words. Still I need to explain my definations.
When I mean "reality", I mean "exact " reality as most people would think.
When I mean "approximation", I mean not as exact or detailed as reality. That's what I mean.
#1274 Help Me ! » Sum of an Infinite Series » 2006-05-14 18:15:24
- George,Y
- Replies: 18
#1275 Re: Help Me ! » integration » 2006-05-13 23:57:20
The paradox is that the limit sign panetrated through the integral sign and left an incomplete infinity 1/x, and continue to influence following steps.
Ricky, prove why that's valid.