t******l
发帖数: 10908 | 1 你没有证明二元逻辑（true / false)在这个搬石头问题上是不是适用 。。。 也就是
说，为啥搬石头问题可以 bijective 到整数集上，为啥不能是 bijective 在实数集上
。。。 或者通俗的说就是搬石头为啥是个离散数学问题而不是连续数学问题 。。。
或者哥们你是不是给康托打个电话先？
: 完备性。。。这难道不就是稍一琢磨的事情。
: 一个恰好搬不动，另一个恰好搬得起来。。。你代入你那个公式算一算？
|
|
M*****e
发帖数: 11621 | 2 证明部分留给你了 :) 不知道这个算不算一页
A_n = {n pairs of parentheses in the Catalan sense}
B_n = {321-avoiding permutations in S_n}
C_n = {n-sequence with c_1 = 1, and 1 <= c_i <= c_{i-1} + 1}
For any t in A_n, let c(t) be the number of components. E.g., ()() has c = 2
, ()()(()) has c = 3.
For any s in B_n, let m(s) be the number of positions one can insert n+1 to
get an element in B_{n+1}. To be more explicit, if s = 123..n, then m(s) =
n+1, otherwise there is a largest j(necessarily <= n-1) that has an i>j... 阅读全帖 |
|
a***n
发帖数: 3633 | 3 请问isomorphism和homomorphism的区别
一个地方说, A one-one mapping f of X onto Y is called a homomorphism
between X and Y if f is continuous and the mapping f-1 inverse to f is also
continuous.
另外一个地方说An isomorphism is a bijective homomorphism. 但是one-one + onto
不就是bijective ?
谢谢 |
|
D******n
发帖数: 2965 | 4 从R^2到R的bijection 有没有可能存在一个是measurable的?
另外关于概率测度，我觉得Boreal Function的方法来定义一个新的变量的
measurability还是非常局限的，人家都bijection出来的，居然是否是random
variable 还成问题。为什么一定要看Boreal set 呢? |
|
w*m
发帖数: 6 | 5 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 |
|
t******l
发帖数: 10908 | 6 狮子没法类比，成年的雌雄比例都不是 1：1。。。两个性别的集合没法 bijection 的
种群，不能归类成女流氓。 |
|
s***h
发帖数: 487 | 7 感觉罪魁祸首在复数本身，加上二维空间 vs 一维空间的本质差别。
复数是实数给 “延拓” 出来的，而且是数集 “延拓” 出来的
第一个不对应于（bijection) 任何物理几何测量的数。
我个人感觉，复数集，是数学从工程学院的测量科学，演变成 Fine Art 学院的美学，
所迈出的关键的一步。
: 一阶可导推出二阶可导，这是解析函数最重要的一个跳跃。这个证明我记
得还是
有点难
: 度的。应该是用来柯西积分公式。 |
|
s***h
发帖数: 487 | 8 这里有两个问题，一个时无限"尺度"的区域，到有限"尺度"的区域的一一映射
bijection。背后的影子是 axiom of choice。
另一个是拓扑映射的 order 保持的问题，加上一个点。
: 谁接一下啊？
|
|
s***h
发帖数: 487 | 9 你这个贴没看到本质问题。这个本质问题就是实数集上的 Axiom of choice，我这不是
开无轨电车，我这么解释。
你上面已经提到了 映射。 你这里的拓扑映射就是实数集合上面的 bijection 。整个
拓扑学就是硬射函数是连续函数， continuous transformation function。
但你不管是怎样的硬射函数，看起来多么 definable，你最终要走到两个实数集之间的
硬射，也就是定义域实数集和值域实数集之间的硬射。
而两个实数集之间的硬射，归根到底就是 axiom of choice 。 而实数集之间的 axiom
of choice ，是没有 definable 的（图灵机刹得住车的）choice function。这就带
来了到底是硬射美胸系花，还是硬射美腿系花，这样的硬射选择困难，因为 choice
function is non-definable（图灵机刹不住车，硬而不射），而最终让数学成为哲学
，或者说，美学。
哥们侃问题要侃本质 。。。
: 复球面无穷远点开集的定义，一句话就定义完了。但是其意义要慢慢展开
，因为
包含的
... 阅读全帖 |
|
H******7
发帖数: 1728 | 10 Theoretical background
You need a Bijective Function f. This is necessary so that you can find a
inverse function g('abc') = 123 for your f(123) = 'abc' function. This means:
There must be no x1, x2 (with x1 ≠ x2) that will make f(x1) = f(x2),
and for every y you must be able to find an x so that f(x) = y.
How to convert the ID to a shortened URL
Think of an alphabet we want to use. In your case that's [a-zA-Z0-9]. It
contains 62 letters.
Take an auto-generated, unique numerical ... 阅读全帖 |
|
u*****a
发帖数: 6276 | 11 Neuroscience is a branch of biology dedicated to studying how the brain
works by focusing on the nervous system and neural networks of humans, in
particular, the neurons and their processes. Scientists have found out that
(1) some brain functions are mainly localized in specific regions of the
brain (“localization”); (2) a region necessary to a particular class of
behaviors/cognition does not mean that it is not involved in other brain
functions or that other brain regions do not contribute to ... 阅读全帖 |
|
l**2
发帖数: 726 | 12
7007教授基础好，以前的东东现在还用得很熟。现在要偶去高考，或者考SAT，GRE偶就
死了。偶只能用最后学得东东，以前学的都已经溢出了。
(x',y')和(x,y)可以是任意坐标，不一定是直角坐标。偶只要映射是把整个扇形映射到
阴影部分（两边都不落下一个点，而且是一个点对一个点 - bijection)。
偶jiao得，这几个圆不同心，用极坐标的话，最多只有一个圆的方程是r=R，其它的都
要涉及角量。或许不一定比直角坐标方便啊。 |
|
M*****e
发帖数: 11621 | 13 为了你严谨的学术态度，我又写了一遍，但我语言组织能力差，看上去似乎更长了……
主要是在C_n <-> B_n 这段，为了和前面的可以无缝连接，我把它反过来写了，原帖
的方向描述更简单些。
A_n = {n pairs of parentheses in the Catalan sense}
B_n = {321-avoiding permutations in S_n}
C_n = {n-integer sequence with c_1 = 1, and 1 <= c_i <= c_{i-1} + 1 for i>=
2}
A_n <-> C_n: take any t in A_n, and reconstruct it according to the order of
“)”, from left to right. The corresponding element in C_n is built by the
number of components c_i at each stage. For example, ()(()) is
reconstructed as ()... 阅读全帖 |
|
l*******s
发帖数: 7316 | 14 A_n = {n pairs of valid parentheses}
B_n = {321-avoiding permutations in S_n}
For any a_i in A_i, c(a_i) is defined as number of pairs of
parentheses in a_i which are not within any other parentheses.
For any a_n in A_n, (c(a_n,1),c(a_n,2),...c(a_n,n)) is called
construction sequence of a_n,
where a_n,i is sub-sequence of a_n made of of first i ")"s
and their corresponding "("s.
For example the construction sequence of ()(()) is (1,2,2)
For any b_i in B_i, c(b_i) is defined as maximum number ele... 阅读全帖 |
|
X****r
发帖数: 3557 | 15 I'm not sure I understand your question here.
For strings a and b we define a relation a <= b iff ab <= ba in
dictionary order. This definition of the relation is useful later,
but only if the relation is a total order, because being a total
order is a necessary and sufficient condition of being able to
sort a finite set ascendingly, i.e. a bijection to [1,n].
(Strictly speaking we need to define equvalent classes to satisty
anti-symmetry)
If the strings can be sorted in s_1,..., s_n, using the |
|
w**a
发帖数: 1024 | 16 what are the Chinese names for these words?
surjective
injective
bijective
onto
thanks. |
|
a**a
发帖数: 416 | 17 for a linear mapping from finite dimension space to finite dimension space,
injective means surjective and thus bijective. |
|
s*******n
发帖数: 740 | 18 哦，忽略了还有continuous这个限制
但是it is really a bijection
is |
|
y**t
发帖数: 50 | 19 for every open subset U of X,we have U intersects A!=empty
or the closure of A is X,A is dense in X
diffeomorphism means there exists a bijective C^{infinity}
map f from top. space X to Y such that f^{-1} is also
C^{infinity}
I wonder if you dunno these 2 concepts,how could you
understand the material you are reading? |
|
