## 胡思乱写

ASW是一个很牛逼的网络，朋友圈子里update的status都是“哎呀，最近看到一艘新的Yacht好喜欢，现在把旧的卖了有人要么”这种status update，呵呵。不过ASW组织的趴体都赞到爆。国内前一阵有人做了一个P1.cn, 照着stureplan.se + sns的模式建的，有点儿ASW的意思，但是用户群体不在一个级别上。

## Cardinality

“长度”“面积”这些词汇究竟是在怎样的意义上被使用的？

·每一个集合都和它自身等势。

·全体正整数的集合和全体正偶数的集合等势。

·全体正整数的集合和全体有理数的集合等势。（什么是有理数来着？查书去！）

·全体正整数的集合和全体实数的集合不等势。

·任给一个无穷集合，我们都能够造出一个集合包含它，而且和它不等势。

·如果两个集合都和第三个集合等势，那么它们彼此也等势。

· 有很多集合都和全体正整数的集合等势，从而它们彼此也等势，我们称所有这样的集合为“可数无穷的（countably infinite）”。有很多无穷集合比全体正整数的集合的势更大，我们称所有这样的集合为不可数无穷的（uncountably infinite）。但是，不存在无穷集合的势比全体正整数的集合的势更小。

·在不可数无穷集合中间，有些集合是和全体实数的集合等势的，这些集合被称为“连续统（continuum）”

In mathematics, the cardinality of a set is a measure of the "number of elements of the set". There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.

Comparing sets

Two sets A and B have the same cardinality if there exists a bijection, that is, an injective and surjective function, from A to B. For example, the set E = {2, 4, 6, …} of positive even numbers has the same cardinality as the set N = {1, 2, 3, …} of natural numbers, since the function f(n) = 2n is a bijection from N to E.

A set A has cardinality greater than or equal to the cardinality of B if there exists an injective function from B into A. The set A has cardinality strictly greater than the cardinality of B if A has cardinality greater than or equal to the cardinality of B, but A and B do not have the same cardinality. In other words, if there is an injective function from B to A, but no bijective function from B to A. For example, the set R of all real numbers has cardinality strictly greater than the cardinality of the set N of all natural numbers, because the inclusion map i : NR is injective, but it can be shown that there does not exist a bijective function from N to R.

## Finite, countable and uncountable sets

If the axiom of choice holds, the law of trichotomy holds for cardinality. Thus we can make the following definitions:

• Any set X with cardinality less than that of the natural numbers (|X| < |N|) is said to be a finite set.
• Any set X that has the same cardinality as the set of the natural numbers (|X| = |N| = ) is said to be a countably infinite set.
• Any set X with cardinality greater than that of the natural numbers (|X| > |N|, for example |R| = > |N|) is said to be uncountable.

## Infinite sets

Our intuition gained from finite sets breaks down when dealing with infinite sets. In the late nineteenth century Georg Cantor, Gottlob Frege, Richard Dedekind and others rejected the view of Galileo (which derived from Euclid) that the whole cannot be the same size as the part. One example of this is Hilbert’s paradox of the Grand Hotel.

Dedekind simply defined an infinite set as one having the same size as at least one of its "proper" parts; this notion of infinity is called Dedekind infinite.

Cantor introduced the above-mentioned cardinal numbers, and showed that some infinite sets are greater than others. The smallest infinite cardinality is that of the natural numbers ().

### Cardinality of the continuum

One of Cantor’s most important results was that the cardinality of the continuum () is greater than that of the natural numbers (); that is, there are more real numbers R than whole numbers N. Namely, Cantor showed that (see Cantor’s diagonal argument).

The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers, that is, . However, this hypothesis can neither be proved nor disproved within the widely accepted ZFC axiomatic set theory, if ZFC is consistent.

Cardinal arithmetic can be used to show not only that the number of points in a real number line is equal to the number of points in any segment of that line, but that this is equal to the number of points on a plane and, indeed, in any finite-dimensional space. These results are highly counterintuitive, because they imply that there exist proper subsets and proper supersets of an infinite set S that have the same size as S, although S contains elements that do not belong to its subsets, and the supersets of S contain elements that are not included in it.

The first of these results is apparent by considering, for instance, the tangent function, which provides a one-to-one correspondence between the interval [-0.5π, 0.5π] and R (see also Hilbert’s paradox of the Grand Hotel).

The second result was first demonstrated by Cantor in 1878, but it became more apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves are not a direct proof that a line has the same number of points as a finite-dimensional space, but they can be easily used to obtain such a proof.

The cardinal equality c2 = c can be demonstrated using cardinal arithmetic: This argument is a condensed version of the notion of interleaving two binary sequences: let be the binary expansion of x and let be the binary expansion of y. Then , the interleaving of the binary expansions, is a well-defined function when x and y have unique binary expansions. Only countably many reals have non-unique binary expansions.

Cantor’s generalized diagonal argument shows that which implies . Here denotes the power set of , the set of all subsets of , and denotes the set of functions from to . Furthermore .

## 交换机，集线器和路由器的区别

（1）工作层次不同

（2）数据转发所依据的对象不同

（3）传统的交换机只能分割冲突域，不能分割广播域；而路由器可以分割广播域

（4）路由器提供了防火墙的服务

一、限定搜索范围的技巧
1、文件类型
2、指定网站
有时我们进行网页搜索，想要在某一个指定的网站内搜索感兴趣的内容，这时候我们可以使用“site”功能来限定搜索的网站。
如果你想把搜索结果限制在大学的网站之中，可以使用“site:.edu 关键词”。
通过限定搜索范围的方法，我们可以更快更准确的搜索到我们想要的东西。
3、其他限定搜索方法
intitle：搜索关键词（intitle:关键字）只搜索网页标题含有关键词的页面。
inurl：搜索关键词（intitle:关键字）只搜索网页链接含有关键词的页面。
intext：搜索关键词（intext:关键字）只搜索网页body标签中的文本含有关键词的页面。
二、写作辅助小工具