r******n
发帖数: 69 | 1 "看了几本书的解释，还是不敢苟同。"
不用看那么些解释。5楼的证明清楚完整。 |
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s***5
发帖数: 203 | 2 兄弟，不是科班出身的吧？突然想起王元说的常有京郊的农民堵在数学所门口号称解决
了哥德巴赫猜想。学过数学分析的，都知道那几个等价的命题，区间套，海涅-伯莱尔
有限覆盖，戴德金分割。。。等等（不好意思，二十多年前学的，一直又不用，记不全
了）。
下边给一个用区间套的政法，说明区间S=【0，1】不能与自然数一一对应。
假设不然，【0，1】区间所有实数可以存在一个与自然数的一一对应a（n）,n=1,2,3..
..
那么把【0，1】区间三等分为【0，1/3】U【1/3，2/3】U【2/3，1】，必有一子区间不
含a(1),把这个子区间叫S(1)，同样把S(1)区间三等分，必有一子区间不含a(2)，把这
个子区间叫S(2），当然S(2）也不含a(1)。。。依次类推我们得到一族区间套｛S（n）
｝n=1,2,3....
S（n）是长度为1/3的n次方的闭区间，且S（n+1）是S（n）的子区间，S（n）不含a(1)
,a(2),...a(n)
根据区间套定理，最后S（n）会收敛到区间【0，1】的实数x，x满足所有S（n）的特性
，即x不是任何一个a(n)，与a（n）是【0，1】区间所有实数的一个与自... 阅读全帖 |
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Q***5
发帖数: 994 | 3 楼主看来是真心讨论问题，没必要讽刺。
另外，这问题只是关于“势”，没必要用更多的假设。
.. |
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s***5
发帖数: 203 | 4 兄弟批评的对，应该厚道一点。不过我想说的，数学对于没有接受一些起码的系统训练
的民间爱好者，是个较为困难的学科。我说的那几个等价命题，当然和“势”没关系，
只不过可以用来证明这个“势”。你是科班出身，自然明白，（学数分第二学期一开始
就学用那几个等价命题证明），可楼主兄弟闭门造车，哪里晓得？ |
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p**********0
发帖数: 101 | 5 嘿嘿，问题出在可数的定义上了，啥叫可数？啥叫点点点地下去到无穷？这牵涉到数理
逻辑的问题了。这才有了连续统假设后来的“不可解性“。不知有没说对。。。 |
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c*****4
发帖数: 18 | 6 对，从定义上，可数就是与自然数一一对应（双射）。但是你如果问我自然数是啥？我
到现在还没弄清楚…… |
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s****b
发帖数: 2039 | 7 感谢各位回答！
这个数学版，有专业人士，也有业余人士，也有正在学习的。但是请不要说别人闭门造
车。大家一起灌水，您为什么要打击别人呢？难道您和我有仇？ |
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p*****3
发帖数: 52 | 10 As ericusa said, Prelim surg can be used as PGY-1 for many other specialties
. Additionally, I will add Physical Medicine and Rehabilitation (PMR) and
general surgery in his list.
Prelim surg is relatively easier to get by match. But during the scramble,
it will become very hot as well, and you will have less choice or control.
So if I were you, I would apply earlier.
The disadvantage of prelim surg is that, usually it has very heavy working
load and you don't have time to study Step 3. The wor... 阅读全帖 |
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c******r
发帖数: 300 | 11 U[0,1] = \sum\limits_{i=1}B_i/2^i
where B_i are i.i.d Bernoulli. This is not "efficient" though, a slightly
better one is
U[0,1] = \sum\limits_{i=1}D_i/6^i
where the D_i is the result of rolling the dice.
anyway, you need countably infinite discrete random variables to generate
some continuous distribution (considering the entropy) |
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j******n
发帖数: 271 | 12 pdf definition requires a stronger additivity: Countable additivity. |
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s*******r
发帖数: 63 | 13 I'm not sure whether "countable additivity" is sufficient, because F(d\sigma
) may not be 0. |
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D**u
发帖数: 204 | 14 I think so. If the curve C is fairly (piecewise) smooth/differentiable, at
each point on the contour let "theta" be the angle of the tangent line.
We can define
F(C) = \integrate g(theta) ds
This question is related to (and different from) a concept called "intrinsic volume" which is also finite additive but not countable additive. The difference is: intrinsic volume is invariant under rigid motions (combinations of rotations and translations), while the construction of F is only invariant under |
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d*j
发帖数: 13780 | 15 GS 的？
呵呵
想想二维空间， （a，b）都是整数， 是不是 countable ?
这是面试官给的答案， 很少有人能搞出来吧
stand off the x axis)，有一把枪，可以以每秒1发的速度射击。他看不见车，不知
道车的位置和速度。设计一个algorithm，怎么能eventually hit the car。 |
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t*******e
发帖数: 172 | 16 Is not this G can define a measure on the plane?
For any X we can define G(X)= inf \Sigma G(P_{i}), where inf with respcet to
all the coverings of X by polygons.
Maybe we need G is countable summable.
). |
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x******a
发帖数: 6336 | 18
and use
tanaka's formula:
这样考虑怎么样,错在哪里?
{B_t>0} is a open set of t hence a countable union of open intervals since B
_t is
continuous. on each interval the integral is 0 except for the one have 1 as
an
interior point. it follows the integral should be max(B_1,0). where is the
mistake?
thanks. |
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x******a
发帖数: 6336 | 19 but we know the number of the intervals is countable. |
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d**0
发帖数: 124 | 20 理解了数学上无限可数 countable的概念这题就不难了 |
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d**0
发帖数: 124 | 21 紅書P159, Q5.17
覺得這是考countable概念非常有趣的一題 |
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l**********e
发帖数: 336 | 22 can you share more for this one, how many years of exps after the Warton PhD
?
over these years, there are countable Chinese ppl get in Warton phd program
(finance, etc)
活。 |
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t***a
发帖数: 4 | 23 define open set to be the S-A
S: the space
A: a subset of S; A is finite or countable |
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w*m
发帖数: 6 | 24 有理数集是COUNTABLE的，也就是有理数集
和自然数集的基是相同的，这可以用一个
BIJECTION的函数来证明。
无理数集合的基是UNCOUNTABLE的，不存在
一个BIJECTION函数与自然数集(或有理数集)对应，
这可以用对角线法加以反证。
因此，虽然有理数集和无理数集都是无限上
的概念，但相对来说，无理数集是在更高级上
的无限集，它的基应该和实数集是一致的。
答案应该是0 |
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d*******n
发帖数: 216 | 25 If two distributions have the same expectation and variance, do they have
the same cumulative distribution function? My hunch is not, but cannot
think of an example.( I know the density functions can be different, for
example, at finitely countable points, but I want to know about more general
cases.)
I'd appreciate any help. Thanks! |
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s*****r
发帖数: 790 | 26 You have shown how naive you are about all the concepts here. You have
absolute no understanding of the terminologies you used, except the words
linguistically.
for example, 总体中的个体构成了一个空间，即总体空间。Why this is a space? Do
you know for a set to be a space what properties it should have? do you
know the definition of "space"?
I bet you know nothing about the concepts of countable and uncountable.
btw, your "measure", "measurable", to me sounds like "observation" or
observable.
是学数学的，所以提出来请大家帮忙修正一下，免得... 阅读全帖 |
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s********1
发帖数: 54 | 27 ______________________________________________________________________
In terms of the variance structure
______________________________________________________________________
Normal structure depend on each individual,Spatial structure depends on the
distances between two points and compound, etc.
______________________________________________________________________
In terms of the likelihood:
______________________________________________________________________
The PL method is based on Wol... 阅读全帖 |
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D****r
发帖数: 162 | 29 advice, information, evidence, luggage, news, faculty are non-countable
nouns. There are no advices, informations, evidences, newses, luggages. It
is one piece of advice. one line of evidence. one member of faculty, etc.
When you want to stop someone from revealing his sex life to you, you say
TOO MUCH INFORMATION, not too many informations.
academia is a noun. academic is an adj.
I work in industry or academia.
I prefer the academic setting.
The industrial or academic jobs.
Here is an exp... 阅读全帖 |
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D****r
发帖数: 162 | 30 advice, information, evidence, luggage, news, faculty are non-countable
nouns. There are no advices, informations, evidences, newses, luggages. It
is one piece of advice. one line of evidence. one member of faculty, etc.
When you want to stop someone from revealing his sex life to you, you say
TOO MUCH INFORMATION, not too many informations.
academia is a noun. academic is an adj.
I work in industry or academia.
I prefer the academic setting.
The industrial or academic jobs.
Here is an exp... 阅读全帖 |
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s**g
发帖数: 3271 | 32 u count yourself de ah
or that's too many to be countable??
zan |
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l****e
发帖数: 193 | 33 just happend to finished "the code" as well.
while i was reading on an intustry construction site, i broke
my palm. so i gave up on "Angel and Demons"
i guess he will become a successful pop writer, screenwriter as well
frankly, "the code" is just so so one, but as i am old one
my 2 cents will not be countable as yours. haha
Troy is comming, The force has one year to wait.
may the youth be with you forever!
silence is always the symbol of aged.mature as well.
May the Force be with you! |
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