Enumerated sets
enumeration用法
enumeration用法在编程中,枚举(enumeration)是一种特殊的数据类型,它允许变量有预定义的值之一。
枚举在许多编程语言中都有实现,例如C++、Java、C#等。
使用枚举可以增强代码的可读性和可维护性,同时减少输入错误的可能性。
以下是一个关于如何使用枚举的简单示例:1. 定义枚举类型:首先,我们需要定义一个枚举类型,它包含了一组命名的常量。
这些常量通常是整数或字符,但也可以是其他类型。
例如,在C++中,我们可以定义一个表示星期的枚举类型:```cppenum Weekdays {Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday};```2. 声明枚举变量:接下来,我们可以声明一个枚举类型的变量,并为其赋值。
在这个例子中,我们可以将`currentDay`变量设置为`Monday`:```cppWeekdays currentDay = Monday;```3. 使用枚举变量:现在,我们可以使用枚举变量进行条件判断或其他操作。
例如,我们可以检查`currentDay`是否为周末:```cppif (currentDay == Saturday || currentDay == Sunday) {cout << "It's the weekend!" << endl;} else {cout << "It's a weekday." << endl;}```4. 遍历枚举值:在某些情况下,我们可能需要遍历枚举类型的所有值。
虽然枚举本身不支持直接遍历,但我们可以通过数组或其他容器来实现。
例如,我们可以使用以下方法遍历`Weekdays`枚举的所有值:```cppconst char* weekdayNames[] = {"Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"};for (int i = 0; i < 7; i++) {cout << weekdayNames[i] << endl;}```总之,枚举是一种强大的数据类型,可以帮助我们更好地组织和管理代码中的常量。
十四行诗18英文赏析-莎士比亚
莎士比亚的第18首十四行诗的英文赏析我能否将你比作夏天?你比夏天更美丽温婉。
狂风将五月的蓓蕾凋残,夏日的勾留何其短暂。
休恋那丽日当空,转眼会云雾迷蒙。
休叹那百花飘零,催折于无常的天命。
唯有你永恒的夏日常新,你的美貌亦毫发无损。
死神也无缘将你幽禁,你在我永恒的诗中长存。
只要世间尚有人吟诵我的诗篇,这诗就将不朽,永葆你的芳颜。
这首诗的艺术特点首先是在于它有着双重主题:一是赞美诗人爱友的美貌,二是歌颂了诗歌艺术的不朽力量。
其次就是诗人在诗中运用了新颖的比喻,但又自然而生动。
Sonnet 18, often alternately titled Shall I compare thee to a summer's day?, is one of the best-known of 154 sonnets written by the English playwright and poet William Shakespeare. Part of the Fair Youth sequence (which comprises sonnets 1-126 in the accepted numbering stemming from the first edition in 1609), it is the first of the cycle after the opening sequence now described as the Procreation sonnets. Most scholars now agree that the original subject of the poem, the beloved to whom the poet is writing, is a male, though the poem is commonly used to describe a woman.In the sonnet, the poet compares his beloved to the summer season, and argues that his beloved is better. The poet also states that his beloved will live on forever through the words of the poem. Scholars have found parallels within the poem to Ovid's Tristia and Amores, both of which have love themes. Sonnet 18 is written in the typical Shakespearean sonnet form, having 14 lines of iambic pentameter ending in a rhymed couplet. Detailed exegeses have revealed several double meanings within the poem, giving it a greater depth of interpretation.Sonnet 18 is a typical English or Shakespearean sonnet. It consists of three quatrains followed by a couplet, and has the characteristic rhyme scheme: abab cdcd efef gg. The poem carries the meaning of an Italian or Petrarchan Sonnet. Petrarchan sonnets typically discussed the love and beauty of a beloved, often an unattainable love, but not always.[5] It also contains a volta, or shift in the poem's subject matter, beginning with the third quatrain.A facsimile of the original printing of Sonnet 18.The poem starts with a line of adoration to the beloved—"Shall I compare thee to a summer's day?" The speaker then goes on to say that the beloved being described is both "more lovely and more temperate" than a summer's day. The speaker lists some things that are negative about summer. It is too short—"summer's lease hath alltoo short a date"—and sometimes the sun shines too hot—"Sometime too hot the eye of heaven shines." However, the beloved being described has beauty that will last forever, unlike the fleeting beauty of a summer's day. By putting his love's beauty into the form of poetry, the poet is preserving it forever by the power of his written words. "So long as men can breathe, or eyes can see, So long lives this, and this gives life to thee." The hope is that the two lovers can live on, if not through children, then through the poems brought forth by their love which, unlike children, will not fadeA major feature of this poem - analogy. Begins with the first sentence, put "you" and "Summer" as a analogy, compare the second line of the initial determination: Are you more lovely than the summer, more gentle. The difference is due to produce its in-depth analysis of 3 to 14 lines. Specifically, the first line of 3.4.5.6.7.8 enumerated the "summer" all kinds of regrets, and 9.10.11.12.13.14 line tells the "you" all kinds of advantages compared to the natural draw a final conclusion: "You" is far better than "Summer," "you" because in his poetry between the lines but also has a life, and time forever. Also noteworthy is the verse 13 and 14 are also, by analogy emphasized the "eternal nature."Throughout the poem, the poet freely to the "you" talk, it seems that "you" is a living person, to listen to his voice, understanding his thinking. So this poem can be said to be people in the application of techniques based on the written. The poem "You" refers to an object, academia, there are two explanations, one view is that it refers to beauty, and the other that it refers to poetry to express the good things. Now most scholars prefer the latter.One of the best known of Shakespeare’s sonnets, Sonnet 18 is memorable for the skillful and varied presentation of subject matter, in which the poet’s feelings reach a level of rapture unseen in the previous sonnets. The poet here abandons his quest for the youth to have a child, and instead glories in the youth’s beauty.On the surface, the poem is simply a statement of praise about the beauty of the beloved; summer tends to unpleasant extremes of windiness and heat, but the beloved is always mild and temperate. Summer is incidentally personified as the "eye of heaven" with its "gold complexion"; the imagery throughout is simple and unaffected, with the "darling buds of May" giving way to the "eternal summer", which the speaker promises the beloved. The language, too, is comparatively unadorned for the sonnets; it is not heavy with alliteration or assonance, and nearly every line is its own self-contained clause--almost every line ends with some punctuation, which effects a pause. Initially, the poet poses a question―”Shall I compare thee to a summer’s day?”―and then reflects on it, remarking that the youth’s beauty far surpasses summer’s delights. The imagery is the very essence of simplicity: “wind”and “buds.”In the fourth line, legal terminology―”summer’s lease”―is introduced in contrast to the commonplace images in the first three lines. Note also the poet’s use of extremes in the phrases “more lovely,”“all too short,”and “too hot”; these phrases emphasize the young man’s beauty.Although lines 9 through 12 are marked by a more expansive tone and deeper feeling, the poet returns to the simplicity of the opening images. As one expects in Shakespeare’s sonnets, the proposition that the poet sets up in the first eight lines―that all nature is subject to imperfection―is now contrasted in these next four lines beginning with “But.”Although beauty naturally declines at some point―”And every fair from fair sometime declines”―the youth’s beauty will not; his unchanging appearance is atypical of nature’s steady progression. Even death is impotent against the youth’s beauty. Note the ambiguity in the phrase “eternal lines”: Are these “lines”the poet’s verses or the youth’s hoped-for children? Or are they simply wrinkles meant to represent the process of aging? Whatever the answer, the poet is jubilant in this sonnet because nothing threatens the young man’s beautiful appearance.Sonnet 18 is the first poem in the sonnets not to explicitly encourage the young man to have children. The "procreation" sequence of the first 17 sonnets ended with the speaker's realization that the young man might not need children to preserve his beauty; he could also live, the speaker writes at the end of Sonnet 17, "in my rhyme." Sonnet 18, then, is the first "rhyme"--the speaker's first attempt to preserve the young man's beauty for all time. An important theme of the sonnet (as it is an important theme throughout much of the sequence) is the power of the speaker's poem to defy time and last forever, carrying the beauty of the beloved down to future generations. The beloved's "eternal summer" shall not fade precisely because it is embodied in the sonnet: "So long as men can breathe or eyes can see," the speaker writes in the couplet, "So long lives this, and this gives life to thee."大多数莎学家认为,是作者赞美好友的超常之美的。
美国政府结构
Structure of U.S Government—美国政府的结构The United States is a republic which operates under federalist system. The national government has specific, enumerated powers, and the fifty sovereign states retain substantial autonomy and authority over their respective citizens and residents. Both the national government and each state government are divided into executive, legislative, and judicial branches. Written constitutions, both federal and state, form a system of separated powers, checksand balances among the branches.美国是一个在联邦体系运转下的共和国。
联邦政府有列举的、具体的权利,而五十个自治州保留了对自己公民和居民的实质主权和职权。
联邦政府和州政府都被划分为行政、立法、司法机构。
无论联邦抑或州,成文宪法形成了这些机构间相互制衡的分权体系。
National-Subnational Relations国家与州的关系Any powers not delegated to the federal government in the U.S. Constitution, nor prohibited by it to the states, are reserved to the states or to the people. (U.S. Const. amend. X. )Nonetheless, the powers of the federal government are extensive.The federal government's authority to regulate interstate commerce (U.S. Const. art. I, sec. 8, cl. 3)makes it the predominant force in environmental regulation. The states, under their general police powers to protect the public health, safety and welfare, also retain substantial independent authority to issue environmental protection laws applicable to their citizens and residents.任何既没有在美国宪法中授权给联邦政府、也没有被宪法禁止授权给各州的权力,是保留给各州或人民的。
enumerate函数
enumera用于遍历序列中的元素以及它们的下标
2.函数说明
enumerate(sequence, [start=0])
sequence -- 一个序列、迭代器或其他支持迭代对象。 start -- 下标起始位置。
1)将可循环序列sequence以start开始分别列出序列数据和数据下标。 2)会将该数据对象组合为一个索引序列,同时列出数据和数据下标。
3.实例
import string s = string.ascii_lowercase e = enumerate(s) print(s) print(list(e)) >>> abcdefghijklmnopqrstuvwxyz >>> [(0, 'a'), (1, 'b'), (2, 'c'), (3, 'd'), (4, 'e'), (5, 'f'), (6, 'g'), (7, 'h'), (8, 'i'), (9, 'j'), (10, 'k'), (11, 'l'), (12, 'm'), (13, 'n'), (14, 'o'), (15, 'p'), (16, 'q'), (17, 'r'), (18, 's'), (19, 't'), (20, 'u'), (21, 'v'), (22, 'w' ), (23, 'x'), (24, 'y'), (25, 'z')]
E3 Advanced 9 Empower 自定义字段
Empower 3软件 Advanced 教程 自定义字段提要学完本章以后, 你将能够: 创建一个自定义字段 理解用于自定义字段的选项(例如,字段类型, 数据类型, 峰类型, 样品类型) 对每种类型创建一个自定义字段 学会怎样开发一个更复杂的字段 重要提示: 本培训内容仅仅是为了给你提供一个你创建自己的自定义字段的入门信息什么是自定义字段?字段(field) 是Empower表格中栏目的名称 自定义字段(custom field)是表格中用户定制的字段 自定义字段可以是信息描述也可以是计算公式为何使用自定义字段?想要对保存在Empower 数据库中的样品做特殊的信息标记 想在Empower 的报告中报告样品的特殊信息 想通过自己定制的样品信息来分类或整理数据 想让Empower 执行你自己的计算创建自定义字段所需要的权限自定义字段在项目中创建 操作者必须具有修改项目和创建自定义字段的权限才能创建一个自 定义字段 对于自定义字段有五种特定的权限: 创建, 修改, 删除, 锁定和解锁 自定义字段也可以在报告中体现创建自定义字段的一般流程首先在纸上写出你的自定义字段 在一个实验的项目中实际创建 确认这个自定义字段具有如你所期望的表现 确认后还可以将其拷贝到其它项目创建自定义字段的路径打开Empower的Pro界面 选项目(Projects) > 选配置系统(Configure System) > 右边列表中选中一个项目> 右击 > 属性(Properties) > 出现项目属性对话框> 新建(New) > 选自定义字段(Custom Fields) 栏目 > 跟着向导去做(New Custom Field wizard)即可创建自定义字段的路径点击 配置系统创建自定义字段的路径点击 配置系统创建自定义字段的路径1.选择左边树状 目录中的项目 2.在右边选中一 个项目名字 3.右击 4.选择属性 Properties创建自定义字段的路径5.选择项目属性中的 自定义字段栏目 Custom Fields创建自定义字段的图标说明创建一个自定义字段 修改一个自定义字段 删除一个自定义字段 防止一个自定义字段被修改或允许修改 将一个自定义字段保存到其它的项目 确认修改并退出项目属性 不做修改退出项目属性 查看项目属性的帮助文件创建自定义字段-字段类型字段类型: 样品描述样品,瓶号, 以及样品参数 出现在: 当每个样品的信息都不一样时使用 − 运行样品(Run Samples)窗口的样品表中 − 改变样品(Alter Sample)窗口 − 整数(Integer) − 实数(Real) − 文本(Text)支持的数据类型:− 日期(Date)− 布尔(Boolean)− 枚举(Enumerated)字段类型: 样品还可以在哪里找到样品类型的自定义字段? —查看色谱结果表和通道表 —项目窗口中的以下栏目 —进样(Injections) —结果(Results) —峰(Peaks) —通道(Channels)—签署(Sign Offs)—自定义字段(Custom Fields)字段类型: 样品组标识一个样品组( Sample Set) 当整个数据组的信息都相同时使用 出现在样品组(Sample Set)信息中: — 运行样品(Run Samples)窗口 — 修改样品(Alter Sample)窗口 支持的数据类型: − 实数(Real) − 整数(Integer) − 文本(Text)− 日期(Date)− 布尔(Boolean)− 枚举(Enumerated)字段类型: 样品组样品组类型字段的例子: 色谱柱类型 —样品组方法编辑器 —项目窗口中 还可以在那里找到样品组类型的字段?—样品组(Sample Sets) —进样(Injections) —通道(Channels) —结果(Results) —峰(Peaks)—结果组(Result Sets)—签署(Sign Offs)—自定义字段(Custom Fields)字段类型: 结果用户定义的与结果级别的参数相关的数学计算 每一个色谱/结果有一个答案 支持的数据类型: − 实数(Real) − 文本(Text) 在结果表(Results Table)中出现 − 整数(Integer)− 日期(Date)− 布尔(Boolean)− 枚举(Enumerated)字段类型: 结果结果类型字段的例子: 噪音标准 在项目窗口的下述表中: 还可以在那里找到结果类型的字段? —结果(Results) —峰(Peaks)—签署(Signoffs)字段类型: 组分标识一个被分析物 位于组分编辑器中:— 运行样品(Run Samples)窗口 — 改变样品(Alter Sample)窗口还可在样品组方法编辑器中找到该字段 支持的数据类型: − 实数字段类型: 峰用户定义的与峰相关的数学运算用于峰内计算的字段:Area/Amount用于峰之间计算的字段:Peak Name A[Area]/Peak Name B[Area] 出现在结果表,峰表,签署表中支持的数据类型:−整数(Integer)−实数(Real)−文本(Text)−日期(Date)−布尔(Boolean)−枚举(Enumerated)字段类型: 分布适用于GPC/V 数据的切片参数 根据特定的公式计算支持的数据类型:−实数(Real)−布尔(Boolean)−枚举(Enumerated)−注:本教程不涉及这部分内容你的字段需要哪一种数据类型? 在确定了字段类型后,必须确定该字段的数据类型Integer (0): 整数(不含小数部分)Real (0.0): 实数,浮点数(可以包含小数部分) Text: 文本,包括文字与数字Date: 日期,由用户或由外部来源引入—(例如, 峰字段)布尔: 布尔字段允许将一个数学公式翻译为一个特定值,或由处理而得的答案算符(字段,值),Operator(Field,Value)—两个可能的答案1.是或否2.成功或失败3.由用户定义挑选a.例如:0-超出范围, 1 –在范围内可以翻译到字段中布尔算符:—LT –小于—LTE –小于等于—GT –大于—GTE –大于等于—EQ –等于—NEQ –不等于—RANGE –范围—EQI –大小写不敏感,用于字符串比较—NEQI –大小写不敏感,用于字符串比较枚举: 枚举字段有两个可能的用处:—提供一个包含数值或答案的列表给用户—将多重布尔表达式翻译成一个值或答案枚举(算符(字段,值),算符(字段,值),算符(字段,值))ENUM(Operator(Field,Value),Operator(Field,Value), Operator(Field,Value))例1.创建一个样品类型的新字段字段名称:批号(Lot_Number)目标:使分析者能对每个样品输入批号—为什么是样品类型?—因为此信息对于每个样品都可能是不相同的—其数据类型是什么?相关选项的说明数据来源(Data Source):―键盘(Keyboard): 由分析员输入信息―外部(External): 信息来自另一个数据源(例如,LIMS)―计算(Calculated): 数值由软件计算得来信息必须输入(Data Entry Required):不填入数值,分析员将不能采样 缺省值(Default Value): 此处填入数值,则自动放在此栏目中创建一个样品类型的新字段创建一个样品类型的新字段例2.创建一个样品组类型的新字段字段名称:USP色谱柱类型(USP_Column_Type) 目标: 创建一个USP色谱柱列表以便分析员选用—为什么是样品组类型?—因为此信息对于每个样品都是相同的—其数据类型是什么?查看样品(组)类型自定义字段在样品表中查看批号在样品表中查看色谱柱类型例3:创建组分型自定义字段怎样记录并追踪对照品的纯度?对照品的纯度不是100%进样所用的对照品溶液含有多个对照物质使用组分类型自定义字段用于特定的数字的组分信息键盘或者外部输入比CConst更为方便可用于峰类型或者结果类型的计算峰与结果类型自定义字段的区分峰类型自定义字段是针对峰自行定义的计算用于不同峰之间的运算(峰1面积/峰2面积)用于同一个峰的运算(峰1面积/峰1高度)结果类型自定义字段是与整个样品相关的结果水平参数的自行定义的计算。
NR的MAC层介绍
BSR 8bit Size
DRX(Discontinuous Reception)
drx-Inactivity timer:指定在接收到PDCCH后UE应保持 “ON”的时间。当这个定时器是ON时,UE保持在“ON状 态”,这可以将UE ON周期延长到另外的“OFF”周期。 drx-Retransmission timer:指定UE在第一个可用重传时间 之后应保持活动以等待传入重传的最大连续PDCCH子帧数。
除了固定大小的MAC CE、padding和包 含UL CCCH的MAC SDU外,MAC subheader由四个头字段R/F/LCID/L组 成。 用于固定大小的MAC CE、padding和包 含UL CCCH的MAC SDU,SDU由两个 头字段R/LCID组成。 MAC SDU大小不一。 MAC 子头对应于MAC SDU、MAC CE 或padding。 每个MAC实体每TB最多可传输一个 MAC PDU。
MAC subPDU including MAC subPDU including
including MAC CE 1 including MAC CE 2
MAC SDU
MAC SDU
padding (opt)
R/F/LCID/L subheader
MAC SDU
R/LCID subheader
Fixed-sized MAC CE
DRX的Case4
Case4:Long DRX Cycle 和Short DRX Cycle都配置了,但是循环周期内没有PDCCH被接收。
1. 当配置了C DRX并且最后一个 DCI(PDCCH)到达时;
2. drx inactivityTimer启动,“唤 醒状态”继续,直到drx inactivityTimer过期。
enumerate函数详解
enumerate函数详解中括号内的主题是"enumerate函数详解",以下是一篇1500-2000字的文章,一步一步回答这个主题。
标题:enumerate函数详解:深入理解Python中的枚举函数引言:Python是一门功能强大的编程语言,拥有众多方便实用的内置函数。
其中,enumerate函数是一种常用且强大的函数,用于在迭代过程中获取索引和元素值,使得代码更加简洁高效。
本文将深入介绍enumerate函数的用法和原理,帮助读者更好地理解和应用这个函数。
第一部分:enumerate函数的基本用法enumerate函数是Python的一个内置函数,主要用于将一个可迭代对象转换为一个枚举对象。
其基本语法结构为enumerate(iterable, start=0),其中iterable是要枚举的可迭代对象,而start是一个可选参数,表示开始计数的起始值,缺省时默认为0。
例如,假设我们有一个列表,列表中的元素表示一组学生的姓名。
我们可以使用enumerate函数来同时获取学生的序号和姓名。
pythonstudents = ['Alice', 'Bob', 'Charlie', 'David']for index, student in enumerate(students):print(f"学生{index+1}的姓名是{student}")运行上述代码,输出结果为:学生1的姓名是Alice学生2的姓名是Bob学生3的姓名是Charlie学生4的姓名是David通过enumerate函数,我们可以轻松地获取到学生的序号和姓名。
需要注意的是,序号是从0开始计数的,但我们可以通过修改start参数来改变起始值。
第二部分:enumerate函数的返回值enumerate函数将返回一个枚举对象,它是一个迭代器,可以遍历获取到的元素。
Protege构建本体笔记
Protege构建本体笔记Protege构建本体笔记Protégé构建本体1 3种OWL语言OWL可以分为三种子语言:OWL-Lite,OWL-DL,OWL-Full。
子语言的特征是由它的描述能力来分类的。
其中,OWL-Lite描述能力最弱,OWL-Full描述能力最强,OWL-DL的能力属于中间,同时,OWL-Full可以视为是OWL-DL的一个扩展。
1.1 OWL-Lite在语法上,OWL-Lite是最简单的语言。
一般用于只有一个简单的类层次和定义的约束比较简单的情况。
比如,根据一个现有的百科全书建立的本体。
1.2 OWL-DLOWL-DL是建立在描述逻辑基础上的的,描述能力比OWL-Lite 强得多。
描述逻辑是第一顺序逻辑的决定性部分,可以进行自动推理。
因此,可以自动的计算分类层次,并且检查本体的一致性。
1.3 OWL-FullOWL-Full的表达能力是最强的。
OWL-Full可以适用于需要很强的表达能力的情况。
2 OWL本体的组成OWL本体由个体、关联和类组成,三者分别和实例(Instances)、扩展连接点(Slot)、类(Classes)相通信。
2.1 个体(Individuals)个体就是在领域中,我们所感兴趣的物体。
Protégé和OWL之间有一个显著的区别,就是OWL没有独立名字假定(Unique Name Assumption, UNA)。
这意味着两个不同的名字可以指向同一个个体。
个体就是我们常说的实例,个体可以被理解为“类的实例”。
2.2 关联(Properties)关联指的是两个个体之间的二元关系,比如,一个关联可以把两个个体连接在一起。
例:关联hasSibling,因为Matthew和Gemma是两兄弟,就可以通过hasSibling这个关系把Matthew和Gemma连在了一起,关联也可以只有一个参数,如使某种功能化的关联,如transitive (传递)或symmetric(对称)。
enumerate用法总结-Python3
enumerate⽤法总结-Python3enumerate()说明enumerate()是python的内置函数enumerate在字典上是枚举、列举的意思对于⼀个可迭代的(iterable)/可遍历的对象(如列表、字符串),enumerate将其组成⼀个索引序列,利⽤它可以同时获得索引和值enumerate多⽤于在for循环中得到计数enumerate()使⽤如果对⼀个列表,既要遍历索引⼜要遍历元素时,⾸先可以这样写:1# _*_ coding: utf-8 _*_2# __Author: "LEMON"345 list = ['This', 'is', 'a', 'test']6for i in range(len(list)):7print(i, list[i])上述⽅法有些累赘,利⽤enumerate()会更加直接和优美:1# _*_ coding: utf-8 _*_2# __Author: "LEMON"345 list = ['This', 'is', 'a', 'test']6#for i in range(len(list)):7# print(i, list[i])89for index, item in enumerate(list):10print(index, item)111213 >>>14 0 This15 1 is16 2 a17 3 testenumerate还可以接收第⼆个参数,⽤于指定索引起始值,如:# _*_ coding: utf-8 _*_# __Author: "LEMON"list = ['This', 'is', 'a', 'test']#for i in range(len(list)):# print(i, list[i])#for index, item in enumerate(list):for index, item in enumerate(list,1):print(index, item)>>>1 This2 is3 a4 test补充如果要统计⽂件的⾏数,可以这样写:1 count = len(open(filepath, 'r').readlines())这种⽅法简单,但是可能⽐较慢,当⽂件⽐较⼤时甚⾄不能⼯作。
tqdm enumerate用法
让我们来掇析一下tqdm和enumerate的概念。
tqdm是一个很有用的Python库,它能够让你在循环迭代中显示进度条,让代码执行过程更加直观和具有可视化。
而enumerate则是Python中的内置函数,可以同时获得索引和值,用于在循环中获取索引或者给元素编号。
两者在Python编程中都扮演着不可或缺的角色,让我们一起来深入探讨它们的用法和意义。
1. tqdm的用法及意义让我们来仔细观察一下tqdm的用法和意义。
在Python中,当我们需要在循环中显示进度时,tqdm就能派上用场了。
它的简单易用让我们在处理大规模数据或者进行复杂计算时能够清楚地看到代码的执行进展,从而更加高效地进行编程工作。
通过简单的安装和引入,我们就能在代码中使用tqdm来监视循环的进度,让代码执行的过程更加直观和易于理解。
2. enumerate的用法及意义接下来,我们再来研究一下enumerate的用法和意义。
在实际编程中,有时我们需要获取迭代对象的索引,或者给元素编号,这时enumerate就能派上用场了。
通过使用enumerate,我们可以轻松地同时获得索引和值,从而简化代码逻辑,提高代码的可读性和可维护性。
这对于在循环中需要对元素进行编号或者在处理数据时需要引用索引的情况来说,是非常有益的。
3. 结合使用tqdm和enumerate当我们结合使用tqdm和enumerate时,会有怎样的效果呢?实际上,这样的组合能够让我们在处理大规模数据或者复杂计算时,既能清晰地看到代码的执行进展,又能轻松地获得索引和值,从而更加高效地进行编程工作。
在实际应用中,这样的组合让我们能够更加直观地了解代码的执行过程,同时又能方便地进行数据处理和分析,是非常有价值的。
总结回顾tqdm和enumerate作为Python编程中常用的工具,在循环迭代中都发挥着重要的作用。
通过对它们的深入理解和灵活运用,我们能够更加高效地进行编程工作,提高代码的可读性和可维护性。
Python enumerate() 函数
返回值
返回 enumerate(枚举) 对象。
实例
以下展示了使用 enumerate() 方法的实例:
>>> seasons = ['Spring', 'Summer', 'Fall', 'Winter']
>>> list(enumerate(seasons))
[(0, 'Spring'), (1, 'Summer'), (2, 'Fall'), (3, 'Winter')]
>>> list(enumerate(seasons, start=1))
# 下标从 1 开始
[(1, 'Spring'), (2, 'Summer'), (3, 'Fall'), (4, 'Winter')]
普通的 for 循环
>>> i = 0
>>> seq = ['one', 'two', 'three']
>>> for element in seq:
...
print i, seq[i]
...
i += 1
... 0 one 1 two 2 three
for 循环使用 enumerate
>>> seq = ['one', 'two', 'three']
十四行诗18英文赏析-莎士比亚
莎士比亚的第18首十四行诗的英文赏析我能否将你比作夏天?你比夏天更美丽温婉。
狂风将五月的蓓蕾凋残,夏日的勾留何其短暂。
休恋那丽日当空,转眼会云雾迷蒙。
休叹那百花飘零,催折于无常的天命。
唯有你永恒的夏日常新,你的美貌亦毫发无损。
死神也无缘将你幽禁,你在我永恒的诗中长存。
只要世间尚有人吟诵我的诗篇,这诗就将不朽,永葆你的芳颜。
这首诗的艺术特点首先是在于它有着双重主题:一是赞美诗人爱友的美貌,二是歌颂了诗歌艺术的不朽力量。
其次就是诗人在诗中运用了新颖的比喻,但又自然而生动。
Sonnet 18, often alternately titled Shall I compare thee to a summer's day?, is one of the best-known of 154 sonnets written by the English playwright and poet William Shakespeare. Part of the Fair Youth sequence (which comprises sonnets 1-126 in the accepted numbering stemming from the first edition in 1609), it is the first of the cycle after the opening sequence now described as the Procreation sonnets. Most scholars now agree that the original subject of the poem, the beloved to whom the poet is writing, is a male, though the poem is commonly used to describe a woman.In the sonnet, the poet compares his beloved to the summer season, and argues that his beloved is better. The poet also states that his beloved will live on forever through the words of the poem. Scholars have found parallels within the poem to Ovid's Tristia and Amores, both of which have love themes. Sonnet 18 is written in the typical Shakespearean sonnet form, having 14 lines of iambic pentameter ending in a rhymed couplet. Detailed exegeses have revealed several double meanings within the poem, giving it a greater depth of interpretation.Sonnet 18 is a typical English or Shakespearean sonnet. It consists of three quatrains followed by a couplet, and has the characteristic rhyme scheme: abab cdcd efef gg. The poem carries the meaning of an Italian or Petrarchan Sonnet. Petrarchan sonnets typically discussed the love and beauty of a beloved, often an unattainable love, but not always.[5] It also contains a volta, or shift in the poem's subject matter, beginning with the third quatrain.A facsimile of the original printing of Sonnet 18.The poem starts with a line of adoration to the beloved—"Shall I compare thee to a summer's day?" The speaker then goes on to say that the beloved being described is both "more lovely and more temperate" than a summer's day. The speaker lists some things that are negative about summer. It is too short—"summer's lease hath alltoo short a date"—and sometimes the sun shines too hot—"Sometime too hot the eye of heaven shines." However, the beloved being described has beauty that will last forever, unlike the fleeting beauty of a summer's day. By putting his love's beauty into the form of poetry, the poet is preserving it forever by the power of his written words. "So long as men can breathe, or eyes can see, So long lives this, and this gives life to thee." The hope is that the two lovers can live on, if not through children, then through the poems brought forth by their love which, unlike children, will not fadeA major feature of this poem - analogy. Begins with the first sentence, put "you" and "Summer" as a analogy, compare the second line of the initial determination: Are you more lovely than the summer, more gentle. The difference is due to produce its in-depth analysis of 3 to 14 lines. Specifically, the first line of 3.4.5.6.7.8 enumerated the "summer" all kinds of regrets, and 9.10.11.12.13.14 line tells the "you" all kinds of advantages compared to the natural draw a final conclusion: "You" is far better than "Summer," "you" because in his poetry between the lines but also has a life, and time forever. Also noteworthy is the verse 13 and 14 are also, by analogy emphasized the "eternal nature."Throughout the poem, the poet freely to the "you" talk, it seems that "you" is a living person, to listen to his voice, understanding his thinking. So this poem can be said to be people in the application of techniques based on the written. The poem "You" refers to an object, academia, there are two explanations, one view is that it refers to beauty, and the other that it refers to poetry to express the good things. Now most scholars prefer the latter.One of the best known of Shakespeare’s sonnets, Sonnet 18 is memorable for the skillful and varied presentation of subject matter, in which the poet’s feelings reach a level of rapture unseen in the previous sonnets. The poet here abandons his quest for the youth to have a child, and instead glories in the youth’s beauty.On the surface, the poem is simply a statement of praise about the beauty of the beloved; summer tends to unpleasant extremes of windiness and heat, but the beloved is always mild and temperate. Summer is incidentally personified as the "eye of heaven" with its "gold complexion"; the imagery throughout is simple and unaffected, with the "darling buds of May" giving way to the "eternal summer", which the speaker promises the beloved. The language, too, is comparatively unadorned for the sonnets; it is not heavy with alliteration or assonance, and nearly every line is its own self-contained clause--almost every line ends with some punctuation, which effects a pause. Initially, the poet poses a question―”Shall I compare thee to a summer’s day?”―and then reflects on it, remarking that the youth’s beauty far surpasses summer’s delights. The imagery is the very essence of simplicity: “wind”and “buds.”In the fourth line, legal terminology―”summer’s lease”―is introduced in contrast to the commonplace images in the first three lines. Note also the poet’s use of extremes in the phrases “more lovely,”“all too short,”and “too hot”; these phrases emphasize the young man’s beauty.Although lines 9 through 12 are marked by a more expansive tone and deeper feeling, the poet returns to the simplicity of the opening images. As one expects in Shakespeare’s sonnets, the proposition that the poet sets up in the first eight lines―that all nature is subject to imperfection―is now contrasted in these next four lines beginning with “But.”Although beauty naturally declines at some point―”And every fair from fair sometime declines”―the youth’s beauty will not; his unchanging appearance is atypical of nature’s steady progression. Even death is impotent against the youth’s beauty. Note the ambiguity in the phrase “eternal lines”: Are these “lines”the poet’s verses or the youth’s hoped-for children? Or are they simply wrinkles meant to represent the process of aging? Whatever the answer, the poet is jubilant in this sonnet because nothing threatens the young man’s beautiful appearance.Sonnet 18 is the first poem in the sonnets not to explicitly encourage the young man to have children. The "procreation" sequence of the first 17 sonnets ended with the speaker's realization that the young man might not need children to preserve his beauty; he could also live, the speaker writes at the end of Sonnet 17, "in my rhyme." Sonnet 18, then, is the first "rhyme"--the speaker's first attempt to preserve the young man's beauty for all time. An important theme of the sonnet (as it is an important theme throughout much of the sequence) is the power of the speaker's poem to defy time and last forever, carrying the beauty of the beloved down to future generations. The beloved's "eternal summer" shall not fade precisely because it is embodied in the sonnet: "So long as men can breathe or eyes can see," the speaker writes in the couplet, "So long lives this, and this gives life to thee."大多数莎学家认为,是作者赞美好友的超常之美的。
finite的英文介绍
finite的英文介绍Finite is a term that is commonly used in various fields of mathematics, computer science, and logic. It refers to something that has a definite or limited size, quantity, or extent. In other words, a finite entity is one that can be counted, measured, or enumerated. This concept is in contrast to the idea of infinity, which represents something that is boundless or without end.In mathematics, the term "finite" is used to describe sets, numbers, and functions that have a specific or countable number of elements or values. For example, a finite set is a collection of objects that can be listed or counted, such as the set of natural numbers from 1 to 10. Similarly, a finite number is one that can be expressed as a whole number or a fraction, such as 5, 7/3, or -12. Finite functions, on the other hand, are those that map a finite domain (input) to a finite codomain (output).One of the fundamental concepts in mathematics is the idea of a finite set. A finite set is a collection of distinct objects that can be counted or enumerated. The size or cardinality of a finite set is thenumber of elements it contains. For example, the set {1, 2, 3, 4, 5} is a finite set with a cardinality of 5. Finite sets are often represented using curly braces {} and can be combined using set operations such as union, intersection, and complement.In contrast to finite sets, there are also infinite sets, which are collections of objects that cannot be counted or enumerated. The set of natural numbers (1, 2, 3, ...) and the set of real numbers are examples of infinite sets. These sets have an unlimited number of elements and cannot be exhaustively listed.Another important concept in mathematics is the idea of finite numbers. Finite numbers are those that can be expressed as a whole number or a fraction. These numbers include the natural numbers (1, 2, 3, ...), the integers (0, ±1, ±2, ...), the rational numbers (fractions), and the real numbers (including both rational and irrational numbers). Finite numbers have a specific value and can be compared, added, subtracted, multiplied, and divided.In contrast to finite numbers, there are also infinite numbers, such as the set of real numbers, which cannot be fully enumerated or represented as a single value. These infinite numbers have no definite or countable end and are often used to represent continuous quantities or quantities that cannot be precisely measured.In computer science, the concept of finite is also important. Computers and digital systems are designed to work with finite data, such as binary digits (bits) and finite-precision numbers. The memory and storage capacity of computers are also finite, meaning that they can only store a limited amount of information. Finite state machines, which are fundamental models in computer science, are also based on the idea of finite states and transitions.In logic, the concept of finite is used to describe the size or scope of logical statements and reasoning. A finite logical statement is one that can be completely specified or enumerated, such as "All cats are mammals" or "There exists a prime number greater than 10." In contrast, infinite logical statements, such as "For all natural numbers, there exists a greater natural number," cannot be fully specified or enumerated.The concept of finite is also important in many other fields, such as physics, engineering, and economics. In physics, for example, the finite speed of light and the finite nature of the universe are fundamental concepts. In engineering, the finite capacity of physical systems, such as the limited power output of a generator or the finite storage capacity of a battery, must be taken into account in the design and operation of these systems. In economics, the concept of finite resources, such as limited natural resources or finite laborsupply, is crucial for understanding economic processes and decision-making.In conclusion, the concept of finite is a fundamental idea that underpins many areas of mathematics, computer science, logic, and other fields. It represents the idea of something that is limited, countable, or measurable, in contrast to the concept of infinity, which represents the boundless or unlimited. Understanding the properties and implications of finite entities is essential for solving problems, designing systems, and reasoning about the world around us.。
neo4j set语句
neo4j set语句Neo4j是一款高性能的图数据库,它支持ACID事务、数据持久化以及灵活的数据模型。
在Neo4j中,SET语句主要用于更新图中的节点和关系属性。
SET语句的基本语法如下:1. 更新节点属性:```MATCH (n) WHERE ... SET n.<属性名> = ...```例如,更新节点1的属性`age`为30:```MATCH (n:Person WHERE id(n) = 1) SET n.age = 30```2. 更新关系属性:MATCH (a)-[r]->(b) WHERE ... SET r.<属性名> = ...```例如,更新关系1的属性`weight`为10:```MATCH (a)-[r:LIKES]->(b) WHERE id(r) = 1 SET r.weight = 10```3. 批量更新多个节点或关系属性:```MATCH (n) WHERE ... SET n.<属性名1> = ..., n.<属性名2> = ...```例如,更新节点1的属性`age`为30,同时更新节点2的属性`age`为25:```MATCH (n:Person WHERE id(n) = 1) SET n.age = 30MATCH (n:Person WHERE id(n) = 2) SET n.age = 25请注意,在使用SET语句时,需要确保满足条件的部分确实存在,否则语句将不会执行。
此外,SET语句会直接修改数据库中的数据,因此在执行前请确保已备份数据。
第03章-ASN1基础汇总
标签类型的定义方法
隐式标签通过改变组件类型的标签生成,隐式标 签定义的关键字是IMPLICIT
显式标签通过在组件类型的标签之外添加一个外 部标签生成,显式标签定义的关键字是EXPLICIT ASN.1语法默认使用显式标签
直接方式
新分配一个Tag 基础类型的Tag保留 传输时“双重封装” 语法: <类型名>::=[ [类别名] 标志号] EXPLICIT<基础类 型>
typedef struct _Record {
双方共知的ASN.1定义 Record::=SEQUENCE { phone OCTET STRING, int } BER编码 INTEGER
type Mydata=record
char phone[10];
int age; }Record
phone: string[10];
3.2.1 ASN.1数据类型
简单类型:直接规定取值集合的类型,其中不会 包括任何组件
结构类型:由多个组件构成的类型,每个组件是 一个简单类型或结构类型 标签类型:主要用于区分不同类型数据,特别是 SET中相同类型的组件
ASN.1简单类型
简单类型 INTEGER BOOLEAN REAL ENUMERATED BIT STRING OCTET STRING 类型说明 整数型(正、负整数与0的集合) 布尔型(True与False的集合) 实数型(正、负实数与0的集合) 枚举型(字符串与值的对应关系) 比特流(二进制数组成的比特串) 字节流(十六进制数组成的字节串)
SEQUENCE OF类型定义 <type name>::=SEQUENCE OF <type> <name> IfTable ::= SEQUENCE OF IfEntry
ASN.1基本语法和编码规则
ASN.1基本语法和编码规则1 ASN.1 简介ASN.1 (Abstract Syntax Notation One),抽象语法标记,是描述抽象类型和值的标记,缩写为ASN.1。
它用于对通过接口和通信媒体进行传输的信息的抽象描述,广泛应用于各种通信协议的说明中。
ASN.1是一个很灵活的标记法,它允许定义众多的数据类型——从整数和位串等简单类型到如集合、序列等的组合结构,还可以是其它复杂定义的类型。
一个ASN.1定义可以选用不同的编码规则,但解码器必须采用和编码器相同的编码规则。
目前标准化的编码规则有4个:BER、DER、CER、PER。
BER在19世纪80年代初形成,广泛应用于各种通信协议中,比如SNMP、MHS、TSAPI 等;DER是BER的一种特殊形式,用于对安全性敏感的应用,比如电子商务,要求对一条消息的编码和解码有且只有一条途径;CER是BER 的另一种特殊形式,类似于DER,但它适用于长消息,可以在知道整条消息之前就开始编码,实际中CER很少应用,这是因为工业界把DER作为安全编码的优先方法;PER在上述编码规则之后出现,因它的高效算法而闻名,它的编码速度和压缩程度比BER高,PER适用于带宽资源缺乏的应用,比如空中交通控制和音频—视频通信等。
2 BER的编码规则和传输语法2.1基本规则BER(Basic Encoding Rules)是ASN.1中最早定义的编码规则。
每种BER 编码方法都由三或四部分组成:(1)Tag octets:定义了ASN.1值的类和标签值,并指明编码方法是简单化的还是结构化的。
(2)Length octets:对于定长编码方法,它指出了内容octet的个数;对于结构化、非定长编码方法,它指明了长度是不确定的。
(3)V alue octets:对于简单的、定长编码方法,它给出了值的具体表示;对于结构化的方法,它给出了值的内容的BER编码的串联。
(4)End-of-values octets:对于结构化、非定长的编码方法,它表示内容结束;对于其它方法,没有该部分。
python enumerate用法
python enumerate用法Python是一种高级编程语言,它在数据科学、机器学习、人工智能等领域中被广泛使用。
Python的灵活性和易用性使得它成为了一种非常流行的编程语言。
在Python中,enumerate()是一个非常有用的函数,它可以同时返回列表中的元素和它们的索引值。
在本文中,我们将深入探讨Python enumerate用法。
enumerate()函数是Python中的一个内置函数,它的作用是对一个可迭代对象(如列表、元组、字符串等)进行枚举,同时返回元素和它们的索引值。
下面是一个简单的例子:```fruits = ['apple', 'banana', 'orange']for index, fruit in enumerate(fruits):print(index, fruit)```输出结果:```0 apple1 banana2 orange```在上面的例子中,我们使用了enumerate()函数来遍历一个列表中的元素。
enumerate()函数返回的是一个元组,元组的第一个元素是索引值,第二个元素是列表中的元素。
我们可以使用for循环来遍历这个元组,从而获取列表中的元素和它们的索引值。
除了使用for循环来遍历列表,我们还可以使用list()函数将enumerate()函数返回的结果转换为一个列表。
下面是一个例子:```fruits = ['apple', 'banana', 'orange']enumerate_fruits = list(enumerate(fruits))print(enumerate_fruits)```输出结果:```[(0, 'apple'), (1, 'banana'), (2, 'orange')]```在上面的例子中,我们使用list()函数将enumerate()函数返回的结果转换为了一个列表。
feature_set 析取
feature_set 析取英文回答:Feature set disjunction is a concept in computerscience and machine learning that refers to the combination of multiple feature sets into a single feature set. Inother words, it is the process of merging different sets of features together to create a more comprehensive set of features for analysis or modeling.To understand feature set disjunction, let's consideran example. Imagine we are building a spam email classifier. We have two different feature sets: one set includesfeatures related to the email's subject line, such as the presence of certain keywords or the length of the subject line; the other set includes features related to theemail's content, such as the presence of specific words or phrases.Individually, each feature set provides someinformation about whether an email is spam or not. However, by combining these two feature sets through disjunction, we can create a more powerful and robust feature set that takes into account both the subject line and the content of the email. This combined feature set can then be used to train a machine learning model to classify emails as spam or not.In this example, the feature set disjunction allows us to leverage the strengths of both feature sets and capture a more comprehensive representation of the data. It helps us improve the performance and accuracy of our spam email classifier.中文回答:特征集合析取是计算机科学和机器学习中的一个概念,指的是将多个特征集合合并成一个单一的特征集合。
BER&PER编码规则
/blog/static/21175822008111162436300/3 编码规则和传输语法本章主要介绍BER和PER两种编码规则及其衍生规则。
3.1 BER3.1.1 基本规则BER(Basic Encoding Rules)是ASN.1中最早定义的编码规则,在讨论详细编码规则时,我们是基于正确的抽象描述上。
BER传输语法的格式一直是TLV三元组<Type, Length, Value>也可以认为是<T ag, Length, Value>,见Figure 3-1。
TLV每个域都是一系列八位组,对于组合结构,其中V还可以是TLV三元组,见Figure 3-2。
BER 传输语法是基于八位组(为了避免不同系统上的混淆,没有采用Byte为单位)的,自定界的编码,因为其中L明确界定了八位组的长度。
BER是大端编码的,其八位组的高位比特在左手边,见Figure 3-3。
Figure 3-1 TLV三元组Figure 3-2 传输语法示例Figure 3-3 大端编码BER编码中的T ag(通常是一个八位组),指明了值的类型,其中一个比特表征是基本类型还是组合类型。
T ag有如下两种形式:Figure 3-4 T ag的两种形式当Tag不大于30时,Tag只在一个八位组中编码;当Tag大于30时,则Tag在多个八位组中编码。
在多个八位组中编码时,第一个八位组后五位全部为1,其余的八位组最高位为1表示后续还有,为0表示T ag结束。
Tag的值需要将上图中黄色部分拼接后才能得到。
BER编码中Length表示Value部分所占八位组的个数,有两大类:定长方式(Definite Form)和不定长方式(Indefinite Form);在确定方式中,按照Length所占的八位组个数又分为短、长两种形式。
具体如下:Figure 3-5 Length的三种形式采用定长方式,当长度不大于127个八位组时,Length只在一个八位组中编码;当长度大于127时,在多个八位组中编码,此时第一个八位组低七位表示的是Length所占的长度,后续八位组表示Value的长度。
enumerate()函数 python编程题
在Python编程中,enumerate()函数是一个非常常用的函数。
它的作用是同时获取数据的索引和值,在需要遍历列表、元组或其他可迭代对象时,能够极大地方便编程。
接下来,我将深入探讨enumerate()函数的使用方法、原理和实际应用,并结合个人观点进行详细阐述。
1. enumerate()函数的基本用法在Python中,enumerate()函数的基本语法为:enumerate(iterable, start=0),其中iterable代表要遍历的可迭代对象,start代表索引起始值(默认为0)。
使用enumerate()函数可以直接获取索引和值,如下所示:```pythonmy_list = ['apple', 'banana', 'orange']for index, value in enumerate(my_list):print(index, value)```以上代码将输出:```0 apple1 banana2 orange```这样就能够在循环中同时获取索引和值,非常方便快捷。
2. enumerate()函数的原理和内部实现在Python中,enumerate()函数的内部实现其实是一个迭代器。
它通过调用传入的可迭代对象的__iter__方法,然后再获取迭代器对象的_next__方法来逐个获取可迭代对象的值,并同时生成对应的索引。
这样就实现了在遍历过程中获取索引和值的功能。
3. enumerate()函数在实际应用中的价值enumerate()函数在实际编程中有着非常重要的价值。
在需要对列表、元组等序列进行遍历并且需要同时获取索引和值的情况下,使用enumerate()函数能够简化代码,提高可读性,减少编程出错的可能性。
尤其是在需要对数据进行处理、分析或者统计时,enumerate()函数更是必不可少的工具。
4. 个人观点和理解在我看来,enumerate()函数的设计非常贴心且实用,它提供了一种非常优雅的方式来处理需要索引的循环。
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JOURNAL OF FORMALIZED MATHEMATICSV olume1,Released1989,Published2003Inst.of Computer Science,Univ.of BiałystokEnumerated SetsAndrzej TrybulecWarsaw UniversityBiałystokSummary.We prove basic facts about enumerated sets:definitional theorems and their immediate consequences,some theorems related to the decomposition of an enumeratedset into union of two sets,facts about removing elements that occur more than once,andfacts about permutations of enumerated sets(with the length≤4).The article includes alsoschemes enabling instantiation of up to nine universal quantifiers.MML Identifier:ENUMSET1.WWW:/JFM/Vol1/enumset1.htmlThe article[1]provides the notation and terminology for this paper.In this paper x,x1,x2,x3,x4,x5,x6,x7,x8,X are sets.In this article we present several logical schemes.The scheme UI1deals with a set A and a unary predicate P,and states that:P[A]provided the parameters have the following property:•For every x1holds P[x1].The scheme UI2deals with sets A,B and a binary predicate P,and states that: P[A,B]provided the following condition is satisfied:•For all x1,x2holds P[x1,x2].The scheme UI3deals with sets A,B,C and a ternary predicate P,and states that: P[A,B,C]provided the parameters meet the following condition:•For all x1,x2,x3holds P[x1,x2,x3].The scheme UI4deals with sets A,B,C,D and a4-ary predicate P,and states that: P[A,B,C,D]provided the following requirement is met:•For all x1,x2,x3,x4holds P[x1,x2,x3,x4].The scheme UI5deals with sets A,B,C,D,E and a5-ary predicate P,and states that: P[A,B,C,D,E]provided the following requirement is met:•For all x1,x2,x3,x4,x5holds P[x1,x2,x3,x4,x5].The scheme UI6deals with sets A,B,C,D,E,F and a6-ary predicate P,and states that: P[A,B,C,D,E,F]provided the parameters meet the following condition:•For all x1,x2,x3,x4,x5,x6holds P[x1,x2,x3,x4,x5,x6].The scheme UI7deals with sets A,B,C,D,E,F,G and a7-ary predicate P,and states that: P[A,B,C,D,E,F,G]provided the parameters satisfy the following condition:1c Association of Mizar Users•For all x1,x2,x3,x4,x5,x6,x7holds P[x1,x2,x3,x4,x5,x6,x7].The scheme UI8deals with sets A,B,C,D,E,F,G,H and a8-ary predicate P,and states that:P[A,B,C,D,E,F,G,H]provided the parameters satisfy the following condition:•For all x1,x2,x3,x4,x5,x6,x7,x8holds P[x1,x2,x3,x4,x5,x6,x7,x8].The scheme UI9deals with sets A,B,C,D,E,F,G,H,I and a9-ary predicate P,and states that:P[A,B,C,D,E,F,G,H,I]provided the following condition is satisfied:•For all sets x1,x2,x3,x4,x5,x6,x7,x8,x9holds P[x1,x2,x3,x4,x5,x6,x7,x8,x9].Let us consider x1,x2,x3.The functor{x1,x2,x3}yields a set and is defined as follows: (Def.1)x∈{x1,x2,x3}iff x=x1or x=x2or x=x3.Next we state three propositions:(13)1If x∈{x1,x2,x3},then x=x1or x=x2or x=x3.(14)If x=x1or x=x2or x=x3,then x∈{x1,x2,x3}.(15)For all x1,x2,x3,X such that for every x holds x∈X iff x=x1or x=x2or x=x3holdsX={x1,x2,x3}.Let us consider x1,x2,x3,x4.The functor{x1,x2,x3,x4}yielding a set is defined by:(Def.2)x∈{x1,x2,x3,x4}iff x=x1or x=x2or x=x3or x=x4.We now state three propositions:(18)2If x∈{x1,x2,x3,x4},then x=x1or x=x2or x=x3or x=x4.(19)If x=x1or x=x2or x=x3or x=x4,then x∈{x1,x2,x3,x4}.(20)For all x1,x2,x3,x4,X such that for every x holds x∈X iff x=x1or x=x2or x=x3orx=x4holds X={x1,x2,x3,x4}.Let us consider x1,x2,x3,x4,x5.The functor{x1,x2,x3,x4,x5}yields a set and is defined by: (Def.3)x∈{x1,x2,x3,x4,x5}iff x=x1or x=x2or x=x3or x=x4or x=x5.One can prove the following three propositions:(23)3If x∈{x1,x2,x3,x4,x5},then x=x1or x=x2or x=x3or x=x4or x=x5.(24)If x=x1or x=x2or x=x3or x=x4or x=x5,then x∈{x1,x2,x3,x4,x5}.(25)For every set X such that for every x holds x∈X iff x=x1or x=x2or x=x3or x=x4orx=x5holds X={x1,x2,x3,x4,x5}.Let us consider x1,x2,x3,x4,x5,x6.The functor{x1,x2,x3,x4,x5,x6}yields a set and is defined as follows:(Def.4)x∈{x1,x2,x3,x4,x5,x6}iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6.One can prove the following three propositions:(28)4If x∈{x1,x2,x3,x4,x5,x6},then x=x1or x=x2or x=x3or x=x4or x=x5or x=x6.1The propositions(1)–(12)have been removed.2The propositions(16)and(17)have been removed.3The propositions(21)and(22)have been removed.4The propositions(26)and(27)have been removed.(29)If x=x1or x=x2or x=x3or x=x4or x=x5or x=x6,then x∈{x1,x2,x3,x4,x5,x6}.(30)Let X be a set.Suppose that for every x holds x∈X iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6.Then X={x1,x2,x3,x4,x5,x6}.Let us consider x1,x2,x3,x4,x5,x6,x7.The functor{x1,x2,x3,x4,x5,x6,x7}yields a set and is defined as follows:(Def.5)x∈{x1,x2,x3,x4,x5,x6,x7}iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7.The following propositions are true:(33)5If x∈{x1,x2,x3,x4,x5,x6,x7},then x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7.(34)If x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7,then x∈{x1,x2,x3,x4,x5,x6,x7}.(35)Let X be a set.Suppose that for every x holds x∈X iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7.Then X={x1,x2,x3,x4,x5,x6,x7}.Let us consider x1,x2,x3,x4,x5,x6,x7,x8.The functor{x1,x2,x3,x4,x5,x6,x7,x8}yields a set and is defined as follows:(Def.6)x∈{x1,x2,x3,x4,x5,x6,x7,x8}iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6 or x=x7or x=x8.The following propositions are true:(38)6If x∈{x1,x2,x3,x4,x5,x6,x7,x8},then x=x1or x=x2or x=x3or x=x4or x=x5orx=x6or x=x7or x=x8.(39)If x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7or x=x8,thenx∈{x1,x2,x3,x4,x5,x6,x7,x8}.(40)Let X be a set.Suppose that for every x holds x∈X iff x=x1or x=x2or x=x3or x=x4or x=x5or x=x6or x=x7or x=x8.Then X={x1,x2,x3,x4,x5,x6,x7,x8}.(41){x1,x2}={x1}∪{x2}.(42){x1,x2,x3}={x1}∪{x2,x3}.(43){x1,x2,x3}={x1,x2}∪{x3}.(44){x1,x2,x3,x4}={x1}∪{x2,x3,x4}.(45){x1,x2,x3,x4}={x1,x2}∪{x3,x4}.(46){x1,x2,x3,x4}={x1,x2,x3}∪{x4}.(47){x1,x2,x3,x4,x5}={x1}∪{x2,x3,x4,x5}.(48){x1,x2,x3,x4,x5}={x1,x2}∪{x3,x4,x5}.(49){x1,x2,x3,x4,x5}={x1,x2,x3}∪{x4,x5}.(50){x1,x2,x3,x4,x5}={x1,x2,x3,x4}∪{x5}.(51){x1,x2,x3,x4,x5,x6}={x1}∪{x2,x3,x4,x5,x6}.(52){x1,x2,x3,x4,x5,x6}={x1,x2}∪{x3,x4,x5,x6}.5The propositions(31)and(32)have been removed.6The propositions(36)and(37)have been removed.(53){x1,x2,x3,x4,x5,x6}={x1,x2,x3}∪{x4,x5,x6}.(54){x1,x2,x3,x4,x5,x6}={x1,x2,x3,x4}∪{x5,x6}.(55){x1,x2,x3,x4,x5,x6}={x1,x2,x3,x4,x5}∪{x6}.(56){x1,x2,x3,x4,x5,x6,x7}={x1}∪{x2,x3,x4,x5,x6,x7}.(57){x1,x2,x3,x4,x5,x6,x7}={x1,x2}∪{x3,x4,x5,x6,x7}.(58){x1,x2,x3,x4,x5,x6,x7}={x1,x2,x3}∪{x4,x5,x6,x7}.(59){x1,x2,x3,x4,x5,x6,x7}={x1,x2,x3,x4}∪{x5,x6,x7}.(60){x1,x2,x3,x4,x5,x6,x7}={x1,x2,x3,x4,x5}∪{x6,x7}.(61){x1,x2,x3,x4,x5,x6,x7}={x1,x2,x3,x4,x5,x6}∪{x7}.(62){x1,x2,x3,x4,x5,x6,x7,x8}={x1}∪{x2,x3,x4,x5,x6,x7,x8}.(63){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2}∪{x3,x4,x5,x6,x7,x8}.(64){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2,x3}∪{x4,x5,x6,x7,x8}.(65){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2,x3,x4}∪{x5,x6,x7,x8}.(66){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2,x3,x4,x5}∪{x6,x7,x8}.(67){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2,x3,x4,x5,x6}∪{x7,x8}.(68){x1,x2,x3,x4,x5,x6,x7,x8}={x1,x2,x3,x4,x5,x6,x7}∪{x8}.(69){x1,x1}={x1}.(70){x1,x1,x2}={x1,x2}.(71){x1,x1,x2,x3}={x1,x2,x3}.(72){x1,x1,x2,x3,x4}={x1,x2,x3,x4}.(73){x1,x1,x2,x3,x4,x5}={x1,x2,x3,x4,x5}.(74){x1,x1,x2,x3,x4,x5,x6}={x1,x2,x3,x4,x5,x6}.(75){x1,x1,x2,x3,x4,x5,x6,x7}={x1,x2,x3,x4,x5,x6,x7}.(76){x1,x1,x1}={x1}.(77){x1,x1,x1,x2}={x1,x2}.(78){x1,x1,x1,x2,x3}={x1,x2,x3}.(79){x1,x1,x1,x2,x3,x4}={x1,x2,x3,x4}.(80){x1,x1,x1,x2,x3,x4,x5}={x1,x2,x3,x4,x5}.(81){x1,x1,x1,x2,x3,x4,x5,x6}={x1,x2,x3,x4,x5,x6}.(82){x1,x1,x1,x1}={x1}.(83){x1,x1,x1,x1,x2}={x1,x2}.(84){x1,x1,x1,x1,x2,x3}={x1,x2,x3}.(85){x1,x1,x1,x1,x2,x3,x4}={x1,x2,x3,x4}.(86){x1,x1,x1,x1,x2,x3,x4,x5}={x1,x2,x3,x4,x5}.(87){x1,x1,x1,x1,x1}={x1}.(88){x1,x1,x1,x1,x1,x2}={x1,x2}.(89){x1,x1,x1,x1,x1,x2,x3}={x1,x2,x3}.(90){x1,x1,x1,x1,x1,x2,x3,x4}={x1,x2,x3,x4}.(91){x1,x1,x1,x1,x1,x1}={x1}.(92){x1,x1,x1,x1,x1,x1,x2}={x1,x2}.(93){x1,x1,x1,x1,x1,x1,x2,x3}={x1,x2,x3}.(94){x1,x1,x1,x1,x1,x1,x1}={x1}.(95){x1,x1,x1,x1,x1,x1,x1,x2}={x1,x2}.(96){x1,x1,x1,x1,x1,x1,x1,x1}={x1}.(98)7{x1,x2,x3}={x1,x3,x2}.(99){x1,x2,x3}={x2,x1,x3}.(100){x1,x2,x3}={x2,x3,x1}.(102)8{x1,x2,x3}={x3,x2,x1}.(103){x1,x2,x3,x4}={x1,x2,x4,x3}.(104){x1,x2,x3,x4}={x1,x3,x2,x4}.(105){x1,x2,x3,x4}={x1,x3,x4,x2}.(107)9{x1,x2,x3,x4}={x1,x4,x3,x2}.(108){x1,x2,x3,x4}={x2,x1,x3,x4}.(109){x1,x2,x3,x4}={x2,x1,x4,x3}.(110){x1,x2,x3,x4}={x2,x3,x1,x4}.(111){x1,x2,x3,x4}={x2,x3,x4,x1}.(112){x1,x2,x3,x4}={x2,x4,x1,x3}.(113){x1,x2,x3,x4}={x2,x4,x3,x1}.(116)10{x1,x2,x3,x4}={x3,x2,x1,x4}.(117){x1,x2,x3,x4}={x3,x2,x4,x1}.(118){x1,x2,x3,x4}={x3,x4,x1,x2}.(119){x1,x2,x3,x4}={x3,x4,x2,x1}.(123)11{x1,x2,x3,x4}={x4,x2,x3,x1}.(125)12{x1,x2,x3,x4}={x4,x3,x2,x1}.7The proposition(97)has been removed.8The proposition(101)has been removed.9The proposition(106)has been removed.10The propositions(114)and(115)have been removed.11The propositions(120)–(122)have been removed.12The proposition(124)has been removed.R EFERENCES[1]Andrzej Trybulec.Tarski Grothendieck set theory.Journal of Formalized Mathematics,Axiomatics,1989./JFM/Axiomatics/tarski.html.Received January8,1989Published January2,2004。