### 数学代写|离散数学作业代写discrete mathematics代考|CS3653

statistics-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

## 数学代写|离散数学作业代写discrete mathematics代考|Standard axiom systems and models

Rather than define our own axiom systems and models from scratch, it helps to use ones that already have a track record of consistency and usefulness. Almost all mathematics fits in one of the following models:

• The natural numbers $\mathbb{N}$. These are defined using the Peano axioms, and if all you want to do is count, add, and multiply, you don’t need much else. (If you want to subtract, things get messy.)
• The integers $\mathbb{Z}$. Like the naturals, only now we can subtract. Division is still a problem.
• The rational numbers $\mathbb{Q}$. Now we can divide. But what about $\sqrt{2}$ ?
• The real numbers $\mathbb{R}$. Now we have $\sqrt{2}$. But what about $\sqrt{(-1)}$ ?
• The complex numbers $\mathbb{C}$. Now we are pretty much done. But what if we want to talk about more than one complex number at a time?
• The universe of sets. These are defined using the axioms of set theory, and produce a rich collection of sets that include, among other things, structures equivalent to the natural numbers, the real numbers, collections of same, sets so big that we can’t even begin to imagine what they look like, and even bigger sets so big that we can’t use the usual accepted system of axioms to prove whether they exist or not. Fortunately, in computer science we can mostly stop with finite sets, which makes life less confusing.
• Various alternatives to set theory, like lambda calculus, category theory, or second-order arithmetic. We won’t talk about these, since they generally don’t let you do anything you can’t do already with sets. However, lambda calculus and category theory are both important to know about if you are interested in programming language theory.
In practice, the usual way to do things is to start with sets and then define everything else in terms of sets: e.g., 0 is the empty set, 1 is a particular set with 1 element, 2 a set with 2 elements, etc., and from here we work our way up to the fancier numbers. The idea is that if we trust our axioms for sets to be consistent, then the things we construct on top of them should also be consistent, although if we are not careful in our definitions they may not be exactly the things we think they are.

## 数学代写|离散数学作业代写discrete mathematics代考|Operations on propositions

Propositions by themselves are pretty boring. So boring, in fact, that logicians quickly stop talking about specific propositions and instead haul out placeholder names like $p, q$, or $r$. But we can build slightly more interesting propositions by combining propositions together using various logical connectives, such as:

Negation The negation of $p$ is written as $\neg p$, or sometimes $\sim p,-p$ or $\bar{p}$. It has the property that it is false when $p$ is true, and true when $p$ is false.

Or The or of two propositions $p$ and $q$ is written as $p \vee q$, and is true as long as at least one, or possibly both, of $p$ and $q$ is true. ${ }^2$ This is not always the same as what “or” means in English; in English, “or” often is used for exclusive or which is not true if both $p$ and $q$ are true. For example, if someone says “You will give me all your money or I will stab you with this table knife”, you would be justifiably upset if you turn over all your money and still get stabbed. But a logician would not be at all surprised, because the standard “or” in propositional logic is an inclusive or that allows for both outcomes.

Exclusive or If you want to exclude the possibility that both $p$ and $q$ are true, you can use exclusive or instead. This is written as $p \oplus q$, and is true precisely when exactly one of $p$ or $q$ is true. Exclusive or is not used in classical logic much, but is important for many computing applications, since it corresponds to addition modulo 2 (see §8.3) and has nice reversibility properties (e.g. $p \oplus(p \oplus q)$ always has the same truth-value as $q$ ).

And The and of $p$ and $q$ is written as $p \wedge q$, and is true only when both $p$ and $q$ are true. ${ }^3$ This is pretty much the same as in English, where “I like to eat ice cream and I own a private Caribbean island” is not a true statement when made by most people even though most people like to eat ice cream. The only complication in translating English expressions into logical ands is that logicians can’t tell the difference between “and” and “but”: the statement ” $2+2=4$ but $3+3=6$ ” becomes simply ” $(2+2=4) \wedge(3+3=6)$.”

# 离散数学代写

## 数学代写|离散数学作业代写discrete mathematics代考|Standard axiom systems and models

• 自然数否. 这些是使用 Peano 公理定义的，如果您想做的只是计数、加法和乘法，则不需要太多其他东西。（如果你想减去，事情会变得一团糟。）
• 整数从. 就像自然界一样，只有现在我们才能减去。分区还是个问题。
• 有理数问. 现在我们可以分开了。但是关于2 ?
• 实数R. 现在我们有2. 但是关于(−1)?
• 复数C. 现在我们差不多完成了。但是，如果我们想一次谈论多个复数怎么办？
• 集合的宇宙。这些是使用集合论的公理定义的，并产生丰富的集合集合，其中包括等同于自然数的结构，实数，相同的集合，集合如此之大以至于我们甚至无法开始想象一下它们的样子，甚至更大的集合大到我们无法使用通常接受的公理系统来证明它们是否存在。幸运的是，在计算机科学中，我们大多可以止步于有限集，这样生活就不会那么混乱了。
• 集合论的各种替代方法，如 lambda 演算、范畴论或二阶算术。我们不会谈论这些，因为它们通常不会让你做任何你不能用集合做的事情。但是，如果您对编程语言理论感兴趣，那么了解 lambda 演算和范畴论都很重要。
在实践中，通常的做法是从集合开始，然后根据集合定义其他所有内容：例如，0 是空集，1 是具有 1 个元素的特定集合，2 是具有 2 个元素的集合，等等。 , 从这里开始，我们努力获得更漂亮的数字。这个想法是，如果我们相信我们的集合公理是一致的，那么我们在它们之上构造的东西也应该是一致的，尽管如果我们在定义时不小心，它们可能并不是我们认为的那样。

## 数学代写|离散数学作业代写discrete mathematics代考|Operations on propositions

Or 两个命题的或p和q写成p∨q，并且只要至少有一个，或者可能两个，都是真的p和q是真的。2这并不总是与英语中“或”的意思相同；在英语中，“或”通常用于排他性或两者都不是p和q是真的。例如，如果有人说“你把所有的钱都给我，否则我就用这把餐刀刺伤你”，如果你把所有的钱都交出来，仍然被刺伤，你理所当然地不高兴。但是逻辑学家一点也不会感到惊讶，因为命题逻辑中的标准“或”是一个包容性的或，它允许两种结果。

Exclusive or 如果你想排除两者的可能性p和q是真的，你可以使用独占或代替。这写成p⊕q，并且恰好在其中之一时为真p或者q是真的。异或在经典逻辑中用得不多，但对许多计算应用程序很重要，因为它对应于加法模 2（参见 §8.3）并且具有良好的可逆性（例如p⊕(p⊕q)总是具有相同的真值q ).

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。