b*******8
发帖数: 37364 | 1 【 以下文字转载自 Programming 讨论区 】
发信人: Caravel (克拉维尔), 信区: Programming
标 题: Google AI system proves over 1200 mathematical theorems
发信站: BBS 未名空间站 (Thu Jun 20 13:46:56 2019, 美东)
Google AI system proves over 1200 mathematical theorems
A new and remarkable development here is that several researchers at Google
’s research center in Mountain View, California have now developed an AI
theorem-proving program. Their program works with the HOL-Light theorem
prover, which was used in Hales’ proof of the Kepl... 阅读全帖 |
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n********s
发帖数: 144 | 2 有人鄙视，有人不情愿，看回复：
1
In general, you should expect a relationship between topology and the
number of solutions, so this single fact is not really enough to say that
the two theorems are similar (though they may well be). For instance, the
Weil conjectures connect the number of solutions over finite fields to
suitable topology in form of Weil cohomology theory. – Thierry Zell
yesterday
Why do you think there is so much similarity? – Donu Arapura 22 hours
ago
And which of Faltin... 阅读全帖 |
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p**********1
发帖数: 1458 | 3 Just came across this theorem again, and want to share it with you guys. It'
s an interesting theorem that is not in poker books AFAIK.
It basically says sklansky's fundamental theorem of poker cannot be extended
to multi-way pot. I remember there was a simpler example to explain it,
kinda like prove by contradiction using a toy game.
the setup is like this, 3 players with same stack size, and they can only
push/call/fold. AND, after push/call, a player must turn his cards face up.
Button(hero) ... 阅读全帖 |
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t*h
发帖数: 148 | 4 From: http://en.wikipedia.org/wiki/Theorem
A theorem (IPA pronunciation: ['θɪəɹəm], from vulgar
Latin theōrēma, Greek θεώρημα "spectacle, speculation, theory")
is a proposition that has been or is to be proved on the basis of explicit
assumptions. Proving theorems is a central activity of mathematicians. Note
that "theorem" is distinct from "theory".
A key property of theorems is that they possess proofs, not merely that they
are true. Logically speaking, everything that |
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t****t
发帖数: 6806 | 5 You have to define \begin{theorem} with
\newtheorem{theorem}{Theorem}
(Because latex can't have one environment for each structures, such as
Lemma, Theorem, Proposition, Axiom, Conjecture, etc.) |
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l*****8
发帖数: 2 | 6 A Theorem is a proposition that has been proved, while a proposition may or
may not have been proved. A lemma is the one which will be used to prove the
final result (Theorem) and a corollary is a simple consequence of a theorem
. Unfortunately, proposition has been abused by many. In my own
understanding, when a proposition is proved, it becomes a theorem. So, a
proposition is nothing but a claim to be proved.
This is just my two cents.
corollary 应该是在proposition 之后的吧。thanks. |
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r****o
发帖数: 1950 | 7 我知道proposion是一个命题，是不是相当于assumption?
lemma是不是比较小的定理，lemma是不是一定要放在theorem的前面？如果我有一个比
较小的定理，但是和theorem没什么关系，可以放在theorem的后面吗？
theorem是比较大，比较正式的定理，对把，
corollary是推论，那么它可以是lemma的推论吗？ |
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T********n
发帖数: 528 | 8 Good find - but to clarity it's not as if Sklansky doesn't know this or
doesn't try to educate this. Something close to Morton's Theorem is also
discussed in HEFAP, right after the section on Sklansky's Fundamental
Theorem of Poker, where it says blah blah exception blah blah multiway blah
blah. What Morton's Theorem does though is it gives practical (game example
) ways to think about how to benefit from this. Such as the part about why
suited connectors go up in value, etc. |
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r***r
发帖数: 153 | 10 assumption 是用于限制讨论范围的，证明或者讨论的时候可以说，在这个assumption
下结论成立
proposition 不熟，但是如果翻译成命题的话，应该和assumption不同
lemma 是引理，是用来证明主要定理的中间引理，只是局限于证明用，而不是主要结果
theorem 是定理，是主要要给人看得结果
corollary 是推论，也是给人看或者要用的正式结果，不过感觉上是说证明不费劲，只
是从已有定理简单几步就推导出来的
lemma是用来证明theorem的，corollary是从theorem 推倒出来的，所以一般不大可能
出现lemma的推论吧 |
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n********s
发帖数: 144 | 11 Faltings Theorem 和 Atiyah-Singer Index Theorem怎么那么相似？都是关于方程的
，都是关于方程解的个数的，方程解的个数和空间的拓扑性质有关。为啥呢？
好奇，门外汉请教。 |
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l*********8
发帖数: 4642 | 14 The master theorem concerns recurrence relations of the form:
T(n) = aT(n/b) + f(n) where a>=1, b>1
My question is:
How can I use master theorem on the following recurrence relations?
T(N) = O(N) + T(N/5) + T(7N/10)
Thanks in advance! |
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t*******n
发帖数: 4445 | 15 Just read about it. Very interesting......
===============================================================
The theorem is due to the Bank of Sweden Prize ("Nobel prize in Economics")
winning economist Kenneth Arrow, who proved it in his PhD thesis and
popularized it in his 1951 book Social Choice and Individual Values.
The theorem's content, somewhat simplified, is as follows. A society needs to
agree on a preference order among several different options. Each individual
in the society has his |
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o*******e
发帖数: 186 | 16 想要显示为
Theorem 3.1 : ....
其中3为section #.
用什么样的设置呢？
现在我能够得到的只能是
Theorem 1 : ....
不能把section包括进去。
谢谢。 |
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v***o
发帖数: 51 | 17 他和Segal的那个一般化envelope theorem （Econometrica 02）里定义参数空间t在[0
,1]上。如果目标函数f(x,t)在countable的t属于[0,1]的点上没定义，应该也可以用吧？
我有两种情况：
1.比如参数空间是m属于整个一维实数集，定义一个关于t->m在[0,1]->R上的增函数,两
个端点都没有定义。
2.或者一些constraint和非零效用函数导致某些f(x,t)在某些t点上无定义。
不过，如果2的情况再结合Inada条件导致在某些x上，f(x,t)关于t在包含这些无定义点
上（一般趋于无穷）的区间不能绝对连续。但是f(x,t)在关于t的去除这些无定义点的[
0,1]上区间仍旧绝对连续，是否还可以在这个区间用这个envelope theorem。 |
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p********t
发帖数: 1219 | 18 Bayes' theorem relates the conditional and marginal probabilities of
stochastic events A and B:
Pr(A|B) = {Pr(B|A)×Pr(A)}/{Pr(B)} = {L(A|B)×Pr(A)}/{Pr(B)}
where
L(A|B) = \Pr(B|A)
is the likelihood of A given B for a fixed value of B.
Each term in Bayes' theorem has a conventional name:
* Pr(A) is the prior probability or marginal probability of A. It is "
prior" in the sense that it does not take into account any information about B
.
* Pr(A|B) is the conditional probability of A, gi |
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x**************.
发帖数: 16 | 19 转信站: mitbbs!jiaoyou8.com!mitbbscn
出 处: mitbbs.cn
发信人: symplectic (愁容/梦里不知身是客), 信区: Mathematics
标 题: A new proof of the 4-colour theorem
发信站: 北大未名站 (2004年09月04日00:18:47 星期六) , 站内信件
Just a moment ago, I found a paper on my colleague's desk,
with the following title:
Every planar graph is 4-colourable and 5-choosable
- a joint proof.
The author is Peter Doerre from Germany. He claimed in
the abstract that:
A new straightforward proof of the 4-colour theorem and the 5-choosable theor
em is present |
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BR
发帖数: 4151 | 21 【 以下文字转载自 Economics 讨论区 】
发信人: BR (no), 信区: Economics
标 题: Proposition, Lemma, Theorem
发信站: BBS 未名空间站 (Mon Jan 1 19:41:51 2007)
给Theorem 做铺垫的可以叫lemma，那给proposition 作铺垫的叫什么？claim?corollary 应该是在proposition 之后的吧。thanks. |
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N***l
发帖数: 52 | 22 Theorem 应该是比较重要的结果吧。
听一个教授说发到某种水平的杂志上才能发表Theorem
水平不够的只能发proposition.不知道是不是真的。 |
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z***c
发帖数: 102 | 23 一篇文章的主要结果肯定是Theorem，但是什么情况下用proposition，我觉得大家的理
解都不一样。我导师的习惯是引用别人的都是proposition，自己证明的都是theorem，
倒也简单。 |
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n**h
发帖数: 22 | 24 The Cramer-Wold theorem states that if every fixed linear combination of d
random variables converges to a normal distribution, then the d variables
jointly converges to a multivariate normal distribution. Does this theorem
hold when the dimension d goes to infinity? Thanks. |
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n**h
发帖数: 22 | 25 The Cramer-Wold theorem states that if every fixed linear combination of d
random variables converges to a normal distribution, then the d variables
jointly converges to a multivariate normal distribution. Does this theorem
hold when the dimension d goes to infinity? Thanks. |
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w***a
发帖数: 226 | 26 To apply Ross recovery theorem, the major difficulty is to infer the Arrow-
Debreu transition matrix from option data. Ross is very vague about what he
did regarding his empirical figure and he used OTC data for no good reason
in my view. It is something suspicious. If you try it you will see. The
theorem iteself relies on very strong assumptions which make it almost
nowhere applicable. I wrote this to save your time. |
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m**a
发帖数: 16 | 27 Hey, have you ever read JD Jackson's preface for the second edition? He made a
joke on Green's function. He said he cleared some mistakes in the first
edition as changing from Green's function to Green function, but he kept
Green's theorem unchanged because that's who it belongs to.
I guess when we say Newtonian Mechanics, we intentionally separate it from the
Lagrangian and Hamiltionian formalism; and when we say Newton's mechanics, we
want to distinguish it from Einstein's mechanics.
Hopefully |
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z*********o
发帖数: 541 | 28 我们的毕业考试就有关于theorem的证明题。因为是theorem所以就要搞清楚，担心会有
这道题 |
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h******3
发帖数: 190 | 29 t = Z sqrt(n - 1) / sqrt(W),
Z is standard normal distribution N(0, 1), W is Chi-square distribution
with n - 1 d.f.
z为什么说通过Cochran's theorem, 可以得知Z和W是independent.
我是初学者，看Cochran's theorem的wikipedia page有点晕。可以帮我解释一下么？
谢谢! |
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n**h
发帖数: 22 | 30 The Cramer-Wold theorem states that if every fixed linear combination of d
random variables converges to a normal distribution, then the d variables
jointly converges to a multivariate normal distribution. Does this theorem
hold when the dimension d goes to infinity? Thanks. |
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发帖数: 1 | 31 题目是integrate{1/(x^4+1),x,0,infinity}
我的方法是residue theorem
f(z)=1/(x^4+1)
Resf(z)=-z/4
Resf(z0)+Resf(z1)=-(e^(i Pi/4)+e^(-i Pi/4))/4=-i/2 Sin(Pi/4)
integrate{1/(x^4+1),x,0,infinity}=1/2 integrate{1/(x^4+1),x,-infinity,
infinity}=1/2 2 Pi i (Resf(z0)+Resf(z1))=2^(1/2)*Pi/4 |
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发帖数: 1 | 32 TheMatrix叔叔tan定理是什么？这题目不用residue theorem怎么写？ |
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T*******x
发帖数: 8565 | 33 我不知道tan定理是什么。这题怎么都要用到residue theorem，或者等价形式，或者是
把residue定理展开。 |
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发帖数: 1 | 34 叔叔能详细讲解一下residue theorem吗？
白老头教我的时候我没学好，当时太小了LOL |
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s******y
发帖数: 289 | 35 证明???要死人的
PS: 你是说的 Chebyshev's Theorem 吧 |
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p****r
发帖数: 9164 | 36 does this theorem mainly focus on preflop equality. what about post flop?
Say we have a suited Ace, do we want to see more ppl in the pot to get
better implied odds when we make nuts flush?
turn
to
old
always |
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p**********1
发帖数: 1458 | 37 I think it started out like this, lots of reg complained there were so many
loose callers in limit games that it was hard to beat. morton looked at some
of the examples/hh and eventually got to his example. the conclusions as
stated in wikipedia http://en.wikipedia.org/wiki/Morton's_theorem), are something we're all familiar with. the value of suited connectors (incl. AXs) goes up in multi-way pot, preflop or postflop; it's correct strategy to thin the field when you got a vulnerable made hand ... 阅读全帖 |
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W********m
发帖数: 7793 | 38 This is interest. I will add my 2 cents.
In a multi-way pot situation, someone's mistake can cost you equity. I think
it is fairly straight forward to understand this if we don't worry too much
about hand strength, but think about the hands in a framework of odds/
combination of hands.
Look at the example you give:
"Button(hero) push and show TT.
Small blind call and show KJs. it's a mistake, as KJs
Big blind call and show AQo.
NOW, hero actually is in worst shape, TT 31.357% K... 阅读全帖 |
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F******n
发帖数: 160 | 39 请问有谁了解：
有无关于Whittaker-Shannon-Kotelnikov (W.S.K.) sampling theorem 的经典出处
引用？就是说，要用到这一定理，想给个好的引用出处。搞数学的是叫这WSK 定理，对吧
？
多谢！ |
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f*********g
发帖数: 632 | 40 Chomsky–Schützenberger theorem. If L is a context-free language admitting
an unambiguous context-free grammar, and a_k := | L \ \cap \Sigma^k | is the
number of words of length k in L, then \sum_{k = 0}^\infty a_k x^k is a
power series over \mathbb{N} that is algebraic over \mathbb{Q}(x). |
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w*******i
发帖数: 987 | 41 definition，theorem这些内容都被设在一个盒子里面了，觉得不好看
怎么去掉这个盒子，就好比背景色为透明一样？
谢谢 |
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t*****e
发帖数: 224 | 42 ☆─────────────────────────────────────☆
BR (no) 于 (Mon Jan 1 19:41:51 2007) 提到:
给Theorem 做铺垫的可以叫lemma，那给proposition 作铺垫的叫什么？claim?corollary 应该是在proposition 之后的吧。thanks. |
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x*****o
发帖数: 28 | 43 请教
pappus' centroid theorem在高维(n>3)下是怎么定义或使用的?
V=AS
在高维下,A还是lamina面积,S是轨迹?
如果是轨迹,对规则体,有没有通用的计算轨迹公式?假设知道了lamina
的centroid了...
有么有什么参考书或webpage之类
Thanks in advance! |
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H****h
发帖数: 1037 | 44 我就没弄清Proposition和Theorem的区别。
corollary 应该是在proposition 之后的吧。thanks. |
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z****f
发帖数: 484 | 45 我从前听一个牛教授很严肃地说起过这个问题
theorem一定要是很重要或者证明很难的结果
当然觉得自己证明的都很难那也可以理解 |
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c***r
发帖数: 63 | 47 my conclusion is that you haven't learnt mathematical logic.
or
the
theorem |
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f********t
发帖数: 14 | 50 Suppose that F:R*R->R is twice differentiable in (x,y), with F(x0,y0)=0. The
classical implicit function theorem requires that dF/dy is nonsingular at (
x0,y0).
My question is that: if the regularity does not hold, but dF/dy is strictly
monotone in the small open neiborhood of y0, for a given x=x0, is y(x) still differentiable? [the continuity has already been shown]. Any reference for that?
Many thanks! |
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