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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写离散数学discrete mathematics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写离散数学discrete mathematics代写方面经验极为丰富，各种代写离散数学discrete mathematics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

Bertrand Russell (Fig. 2.1) was a famous British logician, mathematician and philosopher. He was the co-author with Alfred Whitehead of Principia Mathematica, which aimed to derive all of the truths of mathematics from logic. Russell’s paradox was discovered by Bertrand Russell in 1901, and showed that the system of logicism being proposed by Frege (discussed in Chap. 14) contained a contradiction.
Question (Posed by Russell to FreGe)
Is the set of all sets that do not contain themselves as members a set?
Let $A={S$ a set and $S \notin S}$. Is $A \in A$ ? Then $A \in A \Rightarrow A \notin A$ and vice versa. Therefore, a contradiction arises in either case and there is no such set $A$.

Two ways of avoiding the paradox were developed in 1908, and these were Russell’s theory of types and Zermelo set theory. Russell’s theory of types was a response to the paradox by arguing that the set of all sets is ill-formed. Russell developed a hierarchy with individual elements at the lowest level, sets of elements at the next level, sets of sets of elements at the next level and so on. It is then prohibited for a set to contain members of different types.

A set of elements has a different type from its elements, and one cannot speak of the set of all sets that do not contain themselves as members as these are of different types. The other way of avoiding the paradox was Zermelo’s axiomatization of set theory.

Remark Russell’s paradox may also be illustrated by the story of a town that has exactly one barber who is male. The barber shaves all and only those men in town who do not shave themselves. The question is who shaves the barber.

If the barber does not shave himself, then according to the rule he is shaved by the barber (i.e. himself). If he shaves himself, then according to the rule he is not shaved by the barber (i.e. himself).

The paradox occurs due to self-reference in the statement, and a logical examination shows that the statement is a contradiction.

## 数学代写|离散数学作业代写discrete mathematics代考|Computer Representation of Sets

Sets are fundamental building blocks in mathematics, and so the question arises as to how a set is stored and manipulated in a computer. The representation of a set $M$ on a computer requires a change from the normal view that the order of the elements of the set is irrelevant, and we will need to assume a definite order in the underlying universal set $\ell$ from which the set $M$ is defined.

That is, a set is always defined in a computer program with respect to an underlying universal set, and the elements in the universal set are listed in a definite order. Any set $M$ arising in the program that is defined with respect to this universal set. $\mathscr{C}$ is a subset of $\mathscr{l l}$. Next, we show how the set $M$ is stored internally on the computēr.

The set $M$ is represented in a computer as a string of binary digits $b_1 b_2 \ldots b_n$ where $n$ is the cardinality of the universal set $l 6$. The bits $b_i$ (where $i$ ranges over the values $1,2, \ldots n$ ) are determined according to the rule:
$b_i=1$ if $i$ th element of is in $M$;
$b_i=0$ if $i$ the element of is not in $M$.
For example, if $. \ell={1,2, \ldots 10}$ then the representation of $M={1,2,5,8}$ is given by the bit string 1100100100 where this is given by looking at each element of $.16$ in turn and writing down 1 if it is in $M$ and 0 otherwise.

Similarly, the hit string $0,100,101,100$ represents the set $M={2,5,7,8}$, and this is determined by writing down the corresponding element in $/ /$ that corresponds to a 1 in the bit string.

Clearly, there is a one-to-one correspondence between the subsets of.$/ l$ and all possible $n$-bit strings. Further, the set theoretical operations of set union, intersection and complement can be carried out directly with the bit strings (provided that the sets involved are defined with respect to the same universal set). This involves a bitwise ‘or’ operation for set union, a bitwise ‘and’ operation for set intersection and a bitwise ‘not’ operation for the set complement operation.

# 离散数学代写

1908 年开发了两种避免悖论的方法，它们是罗素的类型理论和策梅洛集合论。罗素的类型理论是对悖论的回应，他认为所有集合的集合都是非良构的。罗素开发了一个层次结构，其中最低级别的单个元素，下一层的元素集，下一层的元素集等等。然后禁止集合包含不同类型的成员。

Remark Russell 的悖论也可以通过一个小镇的故事来说明，该小镇只有一位男性理发师。理发师只给镇上所有不刮胡子的人刮胡子。问题是谁给理发师刮胡子。

## 数学代写|离散数学作业代写discrete mathematics代考|Computer Representation of Sets

b一世=1如果一世的第一个元素在米;
b一世=0如果一世的元素不在米.

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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