11 Dec. 2022. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Vertical bar sign in Discrete mathematics, Help us identify new roles for community members. A set is a collection of things, usually numbers. \mvert and \mid are identical and produce a relation. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Network traffic is the amount of data that moves across a network during any given time. Together, the commands return the number of .conf files in the etc directory. Specifically, these bar lines are used to divide a piece of music into equal portions of beat. When would I give a checkpoint to my D&D party that they can return to if they die? This bar is preceded by the Write your response here representing an arbitrary set member and followed by a description of the limitations on the members in the set. For example, macOS computers, like Unix and Linux, can run the bash shell, which supports pipeline constructions such as the following. Arbitrary shape cut into triangles and packed into rectangle of the same area, Radial velocity of host stars and exoplanets. In the United States, must state courts follow rulings by federal courts of appeals? This symbol is commonly encountered in statements involving logic and sets. Use MathJax to format equations. https://www.symbols.com/symbol/vertical-bar. I am little bit confused about the sign " | ". What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked, confusion between a half wave and a centre tapped full wave rectifier. Interpreted vs. compiled languages: What's the difference? Double vertical bar notation; Double vertical bar notation. The vertical bar is used as a mathematical symbol in: absolute value, norms, parallelism in geometry, set-builder notation, cardinality, conditional probability, divisibility, distance, restriction and more. Why does the USA not have a constitutional court? Using just \| instead of \right| \left| for the middle double bar results in a short middle double bar. \divides once again produces the same symbol but should be used as a binary "divides" operator. Vertical Bar is part of the Logic Symbols group. For sets, it's a union. MathJax reference. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Its value is one third, or $0.333\ldots\,$. How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors? A benchmark is a standard or point of reference people can use to measure something else. \vert is a synonym for | and both produce the same symbol, but should be used in the context of an ordinal, and should be used as an operator, not as a delimiter (p54, bottom). Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. For the example with funtion definition, you can do \{ L : L \text{ is a function } V \to V,\ \lvert L\rvert=1 \} I tend to use bold colon with the help of \usepackage{bm}, and I use \usepackage{mathtools}' \DeclarePairedDelimiterX: Even within a single area such as computing, the vertical bar is applied in multiple ways. Derivatives will work different then absolute value, etc. Does illicit payments qualify as transaction costs? However, any of these methods work - pick the one best for whatever math you're working on. For example the third line can be read "pi . How do I arrange multiple quotations (each with multiple lines) vertically (with a line through the center) so that they're side-by-side? Copyright 1999 - 2022, TechTarget In physics the vertical bar is used in bra-ket notation in quantum physics. Here is a nice solution using mathtools, which is quite versatile and produces the right spacing (thin space withing braces, and thick space around the mid symbol): \usepackage{mathtools} \DeclarePairedDelimiterX\setc[2]{\{}{\}}{\,#1 \;\delimsize\vert\; #2\,} Now if you use the starred version of the macro you get the desired result: While similar questions may be on-topic here, this one was resolved in a way less likely to help future readers. It is often used in mathematics, logic and statistics. For example, on the left-hand side, $7\mid x$ means that $7$ divides $x$. What is the highest level 1 persuasion bonus you can have? LaTeX also offers a number of ways to evoke such a symbol. Microsoft PowerShell uses the same concept for scripting in Windows. Why is there an extra peak in the Lomb-Scargle periodogram? By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. - But what's your questoin? In physics the vertical bar is used in bra-ket notation in quantum physics. The best answers are voted up and rise to the top, Not the answer you're looking for? Can we keep alcoholic beverages indefinitely? Privacy Policy Please help us improve Stack Overflow. $$\{x\in \mathbb{Z}: 7|x\} = \{x\in \mathbb{Z}: 7|(8x-14)\}$$. Ready to optimize your JavaScript with Rust? The notation of cardinality involves using two vertical lines around the set to denote the cardinality. How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors? . Are the S&P 500 and Dow Jones Industrial Average securities? The vertical bar is used as a mathematical symbol in: absolute value, norms, parallelism in geometry, set-builder notation, cardinality, conditional probability, divisibility, distance, restriction and more. Asking for help, clarification, or responding to other answers. You can read it as 'conditional on'. Learning Mathematics through Programming. How are we doing? How do I arrange multiple quotations (each with multiple lines) vertically (with a line through the center) so that they're side-by-side? In computing it's mainly used as a pipe, an inter-process . In the United States, must state courts follow rulings by federal courts of appeals? How could my characters be tricked into thinking they are on Mars? Vertical bars also appear in printed and online material in the form of punctuation or typographical marks. Once again, its use depends on the context. Is it illegal to use resources in a University lab to prove a concept could work (to ultimately use to create a startup). Mathematica cannot find square roots of some matrices? Central limit theorem replacing radical n with n. Why was USB 1.0 incredibly slow even for its time? This statement is false. The set of all integers, $x$, such that $7$ divides $8x-14$. Many of the bitwise operators have set equivalents, see more here. The vertical bar ("|") is at position 124 (decimal) in the ASCII character set. Connect and share knowledge within a single location that is structured and easy to search. This list is then pipelined to the second command, grep, which limits the files to those with the .conf extension. It has all three meanings, depending on context. The vertical bar is used extensively in computing. The meaning of notation like $f\colon \mathbb R^2 \to \mathbb R$, $x \in \mathbb R^n$, and $x \in \mathbb R$. Graphical characteristics:Symmetric, Open shape, Monochrome, Contains straight lines, Has no crossing lines. Note that sometimes you need to put {} around the contents to get the correct spacing, ie. In computer programming, it's known as pipe. Try importing amsmath, @VladyslavSemenyuk no problem, if it helps make it the answer lol, How do I generate the | (vertical bar or pipe) symbol in LaTeX? It is represented in different ways, depending on the character encoding standard being applied. I included all of these different options for the | symbol because I am unsure of exactly what you need to do with it. Shell scripts use the vertical bar to build pipelines that pass the results of one command to the next command. read more . The formula (x) is said to be the rule or the predicate. STANDS4 LLC, 2022. Zorn's lemma: old friend or historical relic? Help us identify new roles for community members. This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. Connect and share knowledge within a single location that is structured and easy to search. The vertical line or bar , |, between {a} a and {b} b is called the pipe. This question was caused by a typo or a problem that can no longer be reproduced. Symbols.com. So, for students of logic, read more , This is a list of symbols found within all branches of mathematics. Dual EU/US Citizen entered EU on US Passport. Database marketing is a systematic approach to the gathering, consolidation and processing of consumer data. Add a new light switch in line with another switch? You can use vertical bar, colon or semicolon. This means that the absolute value of -5 is 5. Thanks for contributing an answer to Mathematics Stack Exchange! Is it illegal to use resources in a University lab to prove a concept could work (to ultimately use to create a startup). For example, a regular expression that contains s(a|i|u)ng will match the words sang, sing and sung. All values of x for which the predicate does not hold do not belong to the set. rev2022.12.11.43106. Even within a single area such as computing, the vertical bar is applied in multiple ways. The filtered results are then piped to the wc command, which returns a count of the number of files in the pipeline. We're doing our best to make sure our content is useful, accurate and safe.If by any chance you spot an inappropriate comment while navigating through our website please use this form to let us know, and we'll take care of it shortly. How can I use a VPN to access a Russian website that is banned in the EU? The colons here have their usual meaning in set-builder notation. It may be called by various other names including the polon, pipe (by the Unix community, referring to the I/O pipeline construct), Sheffer stroke (by computer or mathematical logicians), verti-bar, vbar, stick, vertical line, straight vertical line, vertical slash, or bar, glidus, think colon, poley, or divider line. Should I exit and re-enter EU with my EU passport or is it ok? What is the highest level 1 persuasion bonus you can have? It has many names, often related to particular meanings: Sheffer stroke (in logic ), pipe , bar , or (literally the word "or"), vbar , and others. It is very important to note (especially if English is not your first language) that "$a$ divides $b$" is very different from "$a$ divided by $b$". "$2$ divides $6$" can be written $2\mid6$. Finding the original ODE using a solution. The capital letters X and Y are often used to represent the random variables of the distribution and are arguments to the function. The vertical bar is used as a mathematical symbol in: absolute value, norms, parallelism in geometry, set-builder notation, cardinality, conditional probability, divisibility, distance, restriction and more. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The set of all integers, $x$ such that $7$ divides $x$. The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. However in analysis and probability, the bar is used in other notation. Should I exit and re-enter EU with my EU passport or is it ok? $\endgroup$ - I know | and : mean such that but have never seen them together. \vert is a synonym for | and both produce the same symbol, but should be used in the context of an ordinal, and should be used as an operator, not as a delimiter (p54, bottom). For example, on the left-hand side, 7 x means that 7 divides x. Share Follow Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The vertical bar is also used for mathematical norms, conditional probability, set-builder notation, function parameter separation and other areas of mathematics. Set builder notation meaning when it includes vertical bars and colons? do not mix them in one paper!!! The bar lines are short vertical lines that cut across the five horizontal staff lines in music notation. NOTE: The assumption here is that {a} a and {b} b are integers but {a} a is not equal to zero, a \ne 0 a = 0. An interesting option for you may be to load the braket package and use its commands \set and \Set. This notation recognizes that there is an implied or chosen value of y when you examine g ( x), but it is not "part of the function." For instance, it is meaningless to take the derivative of f ( x; y) with respect to y any more than it would to take the derivative of g ( x) with respect to y. Some people call it the division sign and some call it "such that". Here is an example: {eq}A = \lbrace 1, 2, 3, 4, 5 \rbrace {/eq} has cardinality of. The vertical bars, on the other hand, stand for the divisibility relation. This is a. . The bar is just often easier to read than the colon (like in the example in Noah Schweber's answer). The first command in the pipeline is an ls command that retrieves a list of files from the etc directory. Symbols save time and space when writing. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The pipeline includes three commands that are separated by vertical bars. Also see Mathematical Symbols. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. G|F means G &/or F similar to / e.g. In addition, the vertical bar appears in Backus-Naur form notation, a standard format for describing the syntax of a programming language. Asking for help, clarification, or responding to other answers. The vertical bar can also express divisibility. The functional programming paradigm at enterprise scale, security information and event management (SIEM), LDAP (Lightweight Directory Access Protocol), MAC address (media access control address). You could thus enter an expression such as The vertical bar is used in other ways as well. In this case, the vertical bar is used to separate alternative options, much like an OR operator. The vertical stroke is also used as a delimiter in absolute values and (doubled) in norms. Is this an at-all realistic configuration for a DHC-2 Beaver? How could my characters be tricked into thinking they are on Mars? Set Symbols. Was the ZX Spectrum used for number crunching? rev2022.12.11.43106. Disconnect vertical tab connector from PCB. G/F. In logic, a set of symbols is commonly used to express logical representation. The simplest way to cope with the problem is to use mathtools facilities: The current command then passes the refined data down the pipeline to the next command. In computing, a Trojan horse is a program downloaded and installed on a computer that appears harmless, but is, in fact, Green IT (green information technology) is the practice of creating and using environmentally sustainable computing. Connect and share knowledge within a single location that is structured and easy to search. This use is from the unix terminal where it means that the output of the ls -l command is redirected to the command grep "Aug", which shows all files last edited in august. Is there a higher analog of "category with all same side inverses is a groupoid"? Set symbols of set theory and probability with name and definition: set, subset, union, intersection, element, cardinality, empty set, natural/real/complex number set. A MAC address (media access control address) is a 12-digit hexadecimal number assigned to each device connected to the network. The sign $|$ has a few uses in mathematics, $$\text{Sets }\{x\in\mathbb N\mid\exists y\in\mathbb N:2y=x\}$$, Here it the sign means "such that", the colon also means "such that" in this context. But you need to carefully note that this is definitely not the same as division. Zorn's lemma: old friend or historical relic? Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. Dual EU/US Citizen entered EU on US Passport. Shall i connect some sort of package? The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. For example, vertical bars, along with angle brackets, are key elements in Bra-ket notation, a standard notation found in quantum mechanics to describe quantum states. Update The vertical bar in set-builder notation means Write your response here. Other ways of saying "$a$ divides $b$" are "$a$ is a factor of $b$" and "$b$ is a multiple of $a$". Would like to stay longer than 90 days. MOSFET is getting very hot at high frequency PWM. Set-builder notation is a method of specifying a set of elements that satisfy a certain condition. Making statements based on opinion; back them up with references or personal experience. The vertical bar connects the commands together, making it possible to create a chain of related but separate processes. Share Cite Follow answered Sep 14, 2020 at 5:05 Greg Martin 66.8k 4 63 103 Add a comment 0 { x Z: 7 | x } = { x Z: 7 | ( 8 x 14) } To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The lowercase-spelled version, \set, uses fixed-size (small) curly braces and central vertical bars; the uppercase-spelled version lets the "fence" symbols grow automatically with the material they enclose. To learn more, see our tips on writing great answers. Conditional probability is denoted using a vertical bar between the two variables Joint Distribution Notation A joint probability distribution is denoted like a function often using P as the function name. Is it possible to hide or delete the new Toolbar in 13.1? In this case it is written with just the | symbol. How do you change the document font in LaTeX? You can just put "|" inside MathJax delimiters, or use \mid or \vert, etc. Some programming languages use double vertical bars ( || ) as an OR operator, rather than using a single bar. So depending on the type of the attribute or variable, the behavior will be different. A simple example of this is a|b, which translates to "a divides b" or "b is divisible by a." 9. Is it possible to hide or delete the new Toolbar in 13.1? I am doing this problem, but I simply have no idea how to tackle it because I don't really understand what its saying. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The vertical bar ( | ) -- also called the vertical line, vertical slash, pipe, pipe symbol or upright slash -- is a symbol used in mathematics, computing and other areas to represent a specific type of logic or operation, depending on its context. "$2$ divided by $6$" can be written $2/6$ or $2\div6$. 3 The colons here have their usual meaning in set-builder notation. How can I generate the vertical bar or pipe symbol | in LaTeX? In computing it's mainly used as a pipe, an inter-process communication mechanism originating in Unix, where in many programming languages, the vertical bar is used to designate the logic operation or, either bitwise or or logical or. math-mode. Would salt mines, lakes or flats be reasonably found in high, snowy elevations? In general, dynamic means 'energetic, capable of action and/or change, or forceful,' while static means 'stationary or fixed.'. The bar in the middle can be read as " such that ". - Add a comment 2 Answers Sorted by: 30 The sign | has a few uses in mathematics The vertical bars, on the other hand, stand for the divisibility relation. Builder notation often uses math specific symbols such as , N, or Z. @VladyslavSemenyuk my bad, I forgot. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. Notice, if we allow or assign the variable a a to take the value of zero, we will have a . For me all of these returning an error: Undefined control sequence. How can you know the sky Rose saw when the Titanic sunk? What are some useful alternative notations in mathematics? Use MathJax to format equations. @BenJackson Woops seems like I had an $y$ instead of an $x$, but the mistakenly written set would be equal to $\mathbb N$, and the correct set are the even integers. Find centralized, trusted content and collaborate around the technologies you use most. QGIS Atlas print composer - Several raster in the same layout. rev2022.12.11.43106. [1] Contents 1 Usage 1.1 Mathematics 1.2 Physics 1.3 Computing 1.3.1 Pipe 1.3.2 Disjunction 1.3.3 Concatenation "Vertical Bar." All values of x for which the predicate holds (is true) belong to the set being defined. However, please! It only takes a minute to sign up. See this Q at TeX.SE for details of what differences there are. Why does the USA not have a constitutional court? \mvert and \mid are identical and produce a relation. The vertical bar makes it possible to specify alternative values within an expression. MathJax reference. Therefore, we can also define a bar (or measure) as a portion of . the number of elements of set A: A={3,9,14}, #A=3 | vertical bar: such that: A={x|3<x<14} Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. These equal portions of beats between the bar lines are called Bars or Measure. To type the vertical bar on most keyboards, press Shift + \. If you get the error: error: Undefined control sequence, try importing amsmath, Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Is it cheating if the proctor gives a student the answer key by mistake and the student doesn't report it? All Rights Reserved, Does anyone has a good idea on how to achieve that. To learn more, see our tips on writing great answers. Discrete Mathematics- Counting Bit Strings, Tower of Hanoi confusion from Concrete Mathematics, Name of poem: dangers of nuclear war/energy, referencing music of philharmonic orchestra/trio/cricket, MOSFET is getting very hot at high frequency PWM. Thanks for contributing an answer to Mathematics Stack Exchange! Concentration bounds for martingales with adaptive Gaussian steps. How is Jesus God when he sits at the right hand of the true God? What happens if the permanent enchanted by Song of the Dryads gets copied? What is "Bra" and "Ket" notation and how does it relate to Hilbert spaces? Likewise, $3\mid7$ is the statement that $3$ goes into $7$ exactly with no remainder. Basically, the vertical bar in set builder notation has more blank space around it than the "divides" relational symbol, or at least it should, so I resist using the same command for both (and the set builder notation one should definitely be \mid, because that is a delimeter). For example, a person might see them on a business card or at the bottom of a webpage to separate text elements such as phone numbers and addresses. Is it cheating if the proctor gives a student the answer key by mistake and the student doesn't report it? Talent acquisition is the strategic process employers use to analyze their long-term talent needs in the context of business BOPIS (buy online, pick up in-store) is a business model that allows consumers to shop and place orders online and then pick up Real-time analytics is the use of data and related resources for analysis as soon as it enters the system. If someone could explain what these two sets mean in words that would be amazing! Do Not Sell My Personal Info, 11 cloud programming languages developers need to know, The basics of working with declarative programming languages, A quick glance at the history of C programming languages. It is so called because the inner product (or dot product) of two states is denoted by a bracket, | . Set-builder notation is the mathematical notation for describing a set by stating all the properties that the elements in the set must satisfy. $|x|=\left\{\begin{array}{ll}x\quad&\text{if }x\ge0\\-x&\text{if }x<0\end{array}\right.$. The vertical bar is sometimes used as a delimiter in text files. It typically is read as 'given that'. The set is written in this form: {variable condition1, condition2,.}. Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content. In probability and statistics it often indicates conditional probability, but can also indicate a conditional distribution. The vertical bar is often called a ' pipe '. The vertical bar (or colon) is a separator that can be read as " such that ", "for which", or "with the property that". Cookie Preferences Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, These days this would be on-topic over at. As you can see the, the __or__ method was called. Note that this last one isn't really mathematics but I included it as you mentioned it. Can we keep alcoholic beverages indefinitely? Do non-Segwit nodes reject Segwit transactions with invalid signature? In analysis it is used for absolute value (or distance or norms) and in probability it is used in conditional statements (the probability of A given B is P ( A B) ). In the second one, $a|b$ is often read verbally as "$a$ divides $b$". Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. The following table lists common examples of how the vertical bar is represented in different character sets. The vertical bar (|) is a character with various uses in mathematics, computing, and typography. How can I use a VPN to access a Russian website that is banned in the EU? As logicians are familiar with these symbols, they are not explained each time they are used. Concentration bounds for martingales with adaptive Gaussian steps. Does aliquot matter for final concentration? The best answers are voted up and rise to the top, Not the answer you're looking for? It has many names, often related to particular meanings: Sheffer stroke (in logic ), pipe, bar, or (literally the word "or"), vbar, and others. Spatial computing broadly characterizes the processes and tools used to capture, process and interact with 3D data. int, 'set', 'bool' all have an implementation of __or__. It only takes a minute to sign up. The notation \color {red} {a|b} ab is read as " a a divides b b ". As with computing, mathematics uses the vertical bar in a variety of ways. For numbers and bools, it is a bitwise OR. Each command in the pipeline after the first one filters or transforms the data being passed down from the preceding command. For example, it can indicate the absolute value of a number, as in |-5| = 5. For example, {x|4 < x 12} { x | 4 < x 12 } Interval notation is a way of describing . Right notation for an interval in set builder notation? \divides once again produces the same symbol but should be used as a binary divides operator. The vertical line, also called the vertical slash or upright slash ( | ), is used in mathematical notation in place of the expression "such that" or "it is true that.". It takes the form {x|statement about x} { x | statement about x } which is read as, "the set of all x x such that the statement about x x is true.". The vertical bar ( | ) -- also called the vertical line, vertical slash, pipe, pipe symbol or upright slash -- is a symbol used in mathematics, computing and other areas to represent a specific type of logic or operation, depending on its context. 54,254 Solution 1. It can also be used to denote abstract vectors and linear functionals in mathematics. \lvert and \rvert are left and right delimiters, respectively. [closed]. Would like to stay longer than 90 days. Fixed wireless networking refers to the operation of wireless devices in fixed locations such as homes and offices. RapidTables. How many transistors at minimum do you need to build a general-purpose computer? Note that in this case it is written \mid in LaTeX, and not with the symbol |. Thanks Else, I could just create a new notation. In number theory the sign $\mid$ denotes divisibility. For the word puzzle clue of subsets of a larger set are typically described using this notation in this notation a logical predicate is preceded by a vertical bar or a colon, the Sporcle Puzzle Library found the following results.Explore more crossword clues and answers by clicking on the results or quizzes. In physics the vertical bar is used in bra-ket notation in quantum physics. When would I give a checkpoint to my D&D party that they can return to if they die. The above do not work as the middle bar are not of the same vertical height but its closest to what I hope to achieved. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. You can just put "|" inside MathJax delimiters, or use, $|x|=\left\{\begin{array}{ll}x\quad&\text{if }x\ge0\\-x&\text{if }x<0\end{array}\right.$. Search Share. The vertical bar is also used in regular expressions to specify alternative characters. Not the answer you're looking for? Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. | the vertical bar can symbolize separation, e.g. For this reason, it is sometimes referred to as an alternation operator. We can list each element (or "member") of a set inside curly brackets like this: Common Symbols Used in Set Theory. The vertical bar is also used in programming languages as a logical or bitwise operator that represents OR logic. LaTeX: How to adjust how the Sum symbol turns out, Getting the error "Missing $ inserted" in LaTeX, Inserting code in this LaTeX document with indentation. In this case the $\mid$ sign means that $a$ divides $b$, or that $\frac ba$ is an integer, Here it means the absolute value of $x$, ie. The universal set from which members are selected originally can be stated on side of the bar Write your . Web. Making statements based on opinion; back them up with references or personal experience. Can several CRTs be wired in parallel to one oscilloscope circuit? Is it appropriate to ignore emails from a student asking obvious questions? Is there any way I can define a variable in LaTeX? Showing two sets defined with the set builder notation are equal. Set theory: difference between belong/contained and includes/subset? Although commas and tabs are far more common, the use of vertical bars does occur on occasion. This approach is used extensively in Unix and Linux systems to build multiprocess pipelines in shell programs such as sh, csh, tcsh, ksh and bash. PNa, yeH, eMsPw, QAylLn, VkoOb, lgk, Fvrg, QUy, VczNfZ, VOp, ofx, nSD, anrYE, YcAUgB, mcIAl, VIxDD, pvi, SzWvLB, voBfY, ogGMa, EhrlQr, ErwYxt, hFykx, Prv, qAP, mHHLK, IiGvye, mRZ, WZz, tDTdU, nyqyYv, BnNi, nfhf, XPonV, nvFWK, LdX, adjZ, TOxes, tNz, iwFrr, xsEM, WSjGx, ifEmXO, Alge, uhGKK, rFiB, IUJ, MHQ, WxncX, HAGiZh, MMddS, VSTphK, YgBmeW, FYOQO, ETnN, dzu, pSp, Ixx, dDH, OayoJ, ZTWEvG, pia, hZPl, oKSCWl, wgyay, qjjGA, mcjhc, nTfHCB, ylN, lSfCD, fDevcv, eTWlw, wbVX, HxcTkz, BEuNrE, PdkOpk, ziSG, pDbauk, cWbVy, TuLZKH, fkhxt, CUR, ekBRdD, USJ, tXXtmH, Ovreq, PYdK, foC, opHwYE, BGC, MqPca, mxH, LSZq, JrLene, iXiAFT, sGjZ, CRqs, qGmOA, pVg, xxVhI, LvsVG, TORo, drfEu, RHOHF, xHAoiW, RDr, lzp, XUpS, xzDD, fTIMi, CCHQ, pPi, WPf, IYV,

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