vertical bar in set notation

It has many names, often related to particular meanings: Sheffer stroke (in logic ), pipe, bar, or (literally the word "or"), vbar, and others. You could thus enter an expression such as https://www.symbols.com/symbol/vertical-bar. A simple example of this is a|b, which translates to "a divides b" or "b is divisible by a." 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. Why does the USA not have a constitutional court? Each command in the pipeline after the first one filters or transforms the data being passed down from the preceding command. See this Q at TeX.SE for details of what differences there are. The vertical bar is used extensively in computing. In probability and statistics it often indicates conditional probability, but can also indicate a conditional distribution. Although commas and tabs are far more common, the use of vertical bars does occur on occasion. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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. \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). We can list each element (or "member") of a set inside curly brackets like this: Common Symbols Used in Set Theory. The universal set from which members are selected originally can be stated on side of the bar Write your . The vertical bar is also used for mathematical norms, conditional probability, set-builder notation, function parameter separation and other areas of mathematics. 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. read more . 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. Is there any way I can define a variable in LaTeX? 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. 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. This statement is false. How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors? 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. It is represented in different ways, depending on the character encoding standard being applied. Why is there an extra peak in the Lomb-Scargle periodogram? 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. I am doing this problem, but I simply have no idea how to tackle it because I don't really understand what its saying. Finding the original ODE using a solution. The vertical bar is used in other ways as well. The following table lists common examples of how the vertical bar is represented in different character sets. As you can see the, the __or__ method was called. All values of x for which the predicate does not hold do not belong to the set. 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? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Mathematica cannot find square roots of some matrices? "$2$ divides $6$" can be written $2\mid6$. 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.". Does illicit payments qualify as transaction costs? 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. | the vertical bar can symbolize separation, e.g. STANDS4 LLC, 2022. Is it illegal to use resources in a University lab to prove a concept could work (to ultimately use to create a startup). It typically is read as 'given that'. Privacy Policy \mvert and \mid are identical and produce a relation. Zorn's lemma: old friend or historical relic? 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. RapidTables. In this case, the vertical bar is used to separate alternative options, much like an OR operator. . 11 Dec. 2022. As logicians are familiar with these symbols, they are not explained each time they are used. When would I give a checkpoint to my D&D party that they can return to if they die? Use MathJax to format equations. How could my characters be tricked into thinking they are on Mars? The best answers are voted up and rise to the top, Not the answer you're looking for? Why does the USA not have a constitutional court? A MAC address (media access control address) is a 12-digit hexadecimal number assigned to each device connected to the network. In computing it's mainly used as a pipe, an inter-process . The vertical bars, on the other hand, stand for the divisibility relation. - But what's your questoin? How could my characters be tricked into thinking they are on Mars? Should I exit and re-enter EU with my EU passport or is it ok? 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. 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: To learn more, see our tips on writing great answers. $$\{x\in \mathbb{Z}: 7|x\} = \{x\in \mathbb{Z}: 7|(8x-14)\}$$. 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. How are we doing? For example, on the left-hand side, $7\mid x$ means that $7$ divides $x$. The set of all integers, $x$ such that $7$ divides $x$. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. You can use vertical bar, colon or semicolon. int, 'set', 'bool' all have an implementation of __or__. You can read it as 'conditional on'. Dual EU/US Citizen entered EU on US Passport. Many of the bitwise operators have set equivalents, see more here. Can we keep alcoholic beverages indefinitely? Using just \| instead of \right| \left| for the middle double bar results in a short middle double bar. Set-builder notation is a method of specifying a set of elements that satisfy a certain condition. For example, on the left-hand side, 7 x means that 7 divides x. Vertical Bar is part of the Logic Symbols group. I am little bit confused about the sign " | ". This means that the absolute value of -5 is 5. rev2022.12.11.43106. An interesting option for you may be to load the braket package and use its commands \set and \Set. The vertical bar can also express divisibility. Shall i connect some sort of package? Therefore, we can also define a bar (or measure) as a portion of . The vertical stroke is also used as a delimiter in absolute values and (doubled) in norms. 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. MOSFET is getting very hot at high frequency PWM. How do I arrange multiple quotations (each with multiple lines) vertically (with a line through the center) so that they're side-by-side? Database marketing is a systematic approach to the gathering, consolidation and processing of consumer data. However, please! These equal portions of beats between the bar lines are called Bars or Measure. 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. In the United States, must state courts follow rulings by federal courts of appeals? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. MathJax reference. The bar lines are short vertical lines that cut across the five horizontal staff lines in music notation. 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. 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 ". The colons here have their usual meaning in set-builder notation. Showing two sets defined with the set builder notation are equal. 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. This question was caused by a typo or a problem that can no longer be reproduced. For numbers and bools, it is a bitwise OR. Would like to stay longer than 90 days. Notice, if we allow or assign the variable a a to take the value of zero, we will have a . Some people call it the division sign and some call it "such that". Is it illegal to use resources in a University lab to prove a concept could work (to ultimately use to create a startup). So, for students of logic, read more , This is a list of symbols found within all branches of mathematics. Set builder notation meaning when it includes vertical bars and colons? It is often used in mathematics, logic and statistics. I know | and : mean such that but have never seen them together. \lvert and \rvert are left and right delimiters, respectively. In number theory the sign $\mid$ denotes divisibility. Interpreted vs. compiled languages: What's the difference? "$2$ divided by $6$" can be written $2/6$ or $2\div6$. 3 The colons here have their usual meaning in set-builder notation. Does aliquot matter for final concentration? The filtered results are then piped to the wc command, which returns a count of the number of files in the pipeline. The functional programming paradigm at enterprise scale, security information and event management (SIEM), LDAP (Lightweight Directory Access Protocol), MAC address (media access control address). By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. It can also be used to denote abstract vectors and linear functionals in mathematics. Set Symbols. This list is then pipelined to the second command, grep, which limits the files to those with the .conf extension. 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. Graphical characteristics:Symmetric, Open shape, Monochrome, Contains straight lines, Has no crossing lines. Connect and share knowledge within a single location that is structured and easy to search. 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. Derivatives will work different then absolute value, etc. The vertical line or bar , |, between {a} a and {b} b is called the pipe. Note that this last one isn't really mathematics but I included it as you mentioned it. All Rights Reserved, Find centralized, trusted content and collaborate around the technologies you use most. Can we keep alcoholic beverages indefinitely? Is this an at-all realistic configuration for a DHC-2 Beaver? In the United States, must state courts follow rulings by federal courts of appeals? LaTeX also offers a number of ways to evoke such a symbol. The vertical bars, on the other hand, stand for the divisibility relation. However, any of these methods work - pick the one best for whatever math you're working on. Concentration bounds for martingales with adaptive Gaussian steps. Specifically, these bar lines are used to divide a piece of music into equal portions of beat. Disconnect vertical tab connector from PCB. Symbols save time and space when writing. Even within a single area such as computing, the vertical bar is applied in multiple ways. MathJax reference. How many transistors at minimum do you need to build a general-purpose computer? rev2022.12.11.43106. Thanks Else, I could just create a new notation. For example, {x|4 < x 12} { x | 4 < x 12 } Interval notation is a way of describing . The capital letters X and Y are often used to represent the random variables of the distribution and are arguments to the function. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked, confusion between a half wave and a centre tapped full wave rectifier. The bar is just often easier to read than the colon (like in the example in Noah Schweber's answer). 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). Making statements based on opinion; back them up with references or personal experience. How do I arrange multiple quotations (each with multiple lines) vertically (with a line through the center) so that they're side-by-side? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Likewise, $3\mid7$ is the statement that $3$ goes into $7$ exactly with no remainder. For example, a regular expression that contains s(a|i|u)ng will match the words sang, sing and sung. Search Share. But you need to carefully note that this is definitely not the same as division. Builder notation often uses math specific symbols such as , N, or Z. What are some useful alternative notations in mathematics? the number of elements of set A: A={3,9,14}, #A=3 | vertical bar: such that: A={x|3<x<14} This symbol is commonly encountered in statements involving logic and sets. As with computing, mathematics uses the vertical bar in a variety of ways. 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. Ready to optimize your JavaScript with Rust? 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. How were sailing warships maneuvered in battle -- who coordinated the actions of all the sailors? Please help us improve Stack Overflow. Note that in this case it is written \mid in LaTeX, and not with the symbol |. How can you know the sky Rose saw when the Titanic sunk? Are the S&P 500 and Dow Jones Industrial Average securities? The formula (x) is said to be the rule or the predicate. Arbitrary shape cut into triangles and packed into rectangle of the same area, Radial velocity of host stars and exoplanets. $\endgroup$ - Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. For example the third line can be read "pi . G/F. For example, macOS computers, like Unix and Linux, can run the bash shell, which supports pipeline constructions such as the following. Not the answer you're looking for? Its value is one third, or $0.333\ldots\,$. 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. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The vertical bar in set-builder notation means Write your response here. The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. The simplest way to cope with the problem is to use mathtools facilities: Asking for help, clarification, or responding to other answers. 9. \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). How can I use a VPN to access a Russian website that is banned in the EU? The meaning of notation like $f\colon \mathbb R^2 \to \mathbb R$, $x \in \mathbb R^n$, and $x \in \mathbb R$. Microsoft PowerShell uses the same concept for scripting in Windows. To type the vertical bar on most keyboards, press Shift + \. 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. Thanks for contributing an answer to Mathematics Stack Exchange! So depending on the type of the attribute or variable, the behavior will be different. What is the highest level 1 persuasion bonus you can have? This is a. Is it possible to hide or delete the new Toolbar in 13.1? 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. In addition, the vertical bar appears in Backus-Naur form notation, a standard format for describing the syntax of a programming language. The notation of cardinality involves using two vertical lines around the set to denote the cardinality. math-mode. 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. Spatial computing broadly characterizes the processes and tools used to capture, process and interact with 3D data. This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. It only takes a minute to sign up. In this case it is written with just the | symbol. Use MathJax to format equations. In physics the vertical bar is used in bra-ket notation in quantum physics. Set symbols of set theory and probability with name and definition: set, subset, union, intersection, element, cardinality, empty set, natural/real/complex number set. Share Follow Other ways of saying "$a$ divides $b$" are "$a$ is a factor of $b$" and "$b$ is a multiple of $a$". In physics the vertical bar is used in bra-ket notation in quantum physics. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Web. rev2022.12.11.43106. 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) } Should I exit and re-enter EU with my EU passport or is it ok? Vertical bar sign in Discrete mathematics, Help us identify new roles for community members. The vertical bar is also used in regular expressions to specify alternative characters. For sets, it's a union. Fixed wireless networking refers to the operation of wireless devices in fixed locations such as homes and offices. It is so called because the inner product (or dot product) of two states is denoted by a bracket, | . Is it cheating if the proctor gives a student the answer key by mistake and the student doesn't report it? The first command in the pipeline is an ls command that retrieves a list of files from the etc directory. How can I use a VPN to access a Russian website that is banned in the EU? 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. Double vertical bar notation; Double vertical bar notation. Once again, its use depends on the context. Update What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. The vertical bar makes it possible to specify alternative values within an expression. You can just put "|" inside MathJax delimiters, or use, $|x|=\left\{\begin{array}{ll}x\quad&\text{if }x\ge0\\-x&\text{if }x<0\end{array}\right.$. What is the highest level 1 persuasion bonus you can have? Learning Mathematics through Programming. The notation \color {red} {a|b} ab is read as " a a divides b b ". What happens if the permanent enchanted by Song of the Dryads gets copied? 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 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. Do non-Segwit nodes reject Segwit transactions with invalid signature? While similar questions may be on-topic here, this one was resolved in a way less likely to help future readers. The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. Does anyone has a good idea on how to achieve that. G|F means G &/or F similar to / e.g. - Add a comment 2 Answers Sorted by: 30 The sign | has a few uses in mathematics In physics the vertical bar is used in bra-ket notation in quantum physics. In computer programming, it's known as pipe. 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. Dual EU/US Citizen entered EU on US Passport. Even within a single area such as computing, the vertical bar is applied in multiple ways. @VladyslavSemenyuk my bad, I forgot. The current command then passes the refined data down the pipeline to the next command. 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 is also used in programming languages as a logical or bitwise operator that represents OR logic. Making statements based on opinion; back them up with references or personal experience. For me all of these returning an error: Undefined control sequence. 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. The pipeline includes three commands that are separated by vertical bars. Vertical bars also appear in printed and online material in the form of punctuation or typographical marks. Would salt mines, lakes or flats be reasonably found in high, snowy elevations? Network traffic is the amount of data that moves across a network during any given time. When would I give a checkpoint to my D&D party that they can return to if they die. How is Jesus God when he sits at the right hand of the true God? 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: $|x|=\left\{\begin{array}{ll}x\quad&\text{if }x\ge0\\-x&\text{if }x<0\end{array}\right.$. Is there a higher analog of "category with all same side inverses is a groupoid"? Connect and share knowledge within a single location that is structured and easy to search. Help us identify new roles for community members. In logic, a set of symbols is commonly used to express logical representation. The vertical bar is sometimes used as a delimiter in text files. [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 You can just put "|" inside MathJax delimiters, or use \mid or \vert, etc. The best answers are voted up and rise to the top, Not the answer you're looking for? 54,254 Solution 1. do not mix them in one paper!!! The vertical bar (or colon) is a separator that can be read as " such that ", "for which", or "with the property that". Note that sometimes you need to put {} around the contents to get the correct spacing, ie. To learn more, see our tips on writing great answers. What is "Bra" and "Ket" notation and how does it relate to Hilbert spaces? It has all three meanings, depending on context. . Is it possible to hide or delete the new Toolbar in 13.1? [closed]. Is it cheating if the proctor gives a student the answer key by mistake and the student doesn't report it? However in analysis and probability, the bar is used in other notation. Right notation for an interval in set builder notation? \mvert and \mid are identical and produce a relation. A benchmark is a standard or point of reference people can use to measure something else. \divides once again produces the same symbol but should be used as a binary divides operator. 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. Some programming languages use double vertical bars ( || ) as an OR operator, rather than using a single bar. The set is written in this form: {variable condition1, condition2,.}. "Vertical Bar." Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content. Central limit theorem replacing radical n with n. Why was USB 1.0 incredibly slow even for its time? In the second one, $a|b$ is often read verbally as "$a$ divides $b$". Can several CRTs be wired in parallel to one oscilloscope circuit? Zorn's lemma: old friend or historical relic? Was the ZX Spectrum used for number crunching? I included all of these different options for the | symbol because I am unsure of exactly what you need to do with it. Cookie Preferences Add a new light switch in line with another switch? The vertical bar is often called a ' pipe '. The vertical bar ("|") is at position 124 (decimal) in the ASCII character set. 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 set of all integers, $x$, such that $7$ divides $8x-14$. All values of x for which the predicate holds (is true) belong to the set being defined. A set is a collection of things, usually numbers. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Connect and share knowledge within a single location that is structured and easy to search. \divides once again produces the same symbol but should be used as a binary "divides" operator. 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. Would like to stay longer than 90 days. 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 $b$". Here is an example: {eq}A = \lbrace 1, 2, 3, 4, 5 \rbrace {/eq} has cardinality of. How do you change the document font in LaTeX? 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) ). Copyright 1999 - 2022, TechTarget Shell scripts use the vertical bar to build pipelines that pass the results of one command to the next command. Asking for help, clarification, or responding to other answers. Set theory: difference between belong/contained and includes/subset? How can I generate the vertical bar or pipe symbol | in LaTeX? It only takes a minute to sign up. @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. It has many names, often related to particular meanings: Sheffer stroke (in logic ), pipe , bar , or (literally the word "or"), vbar , and others. Is it appropriate to ignore emails from a student asking obvious questions? QGIS Atlas print composer - Several raster in the same layout. Set-builder notation is the mathematical notation for describing a set by stating all the properties that the elements in the set must satisfy. For example, it can indicate the absolute value of a number, as in |-5| = 5. 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. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The vertical bar (|) is a character with various uses in mathematics, computing, and typography. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Together, the commands return the number of .conf files in the etc directory. Thanks for contributing an answer to Mathematics Stack Exchange! The vertical bar connects the commands together, making it possible to create a chain of related but separate processes. Also see Mathematical Symbols. Concentration bounds for martingales with adaptive Gaussian steps. Symbols.com. For this reason, it is sometimes referred to as an alternation operator. tIlJm, PakVyF, FxVZ, emJq, JSiI, GttzKX, RlRY, mUgk, pHF, VcwEt, UNBmHV, HooXM, XHl, fqD, MhV, ryJCtA, UQW, tKN, KriZa, ZrA, HBhhR, pQkw, Trbgn, bUxs, pMuIc, SBADf, gLTSxw, kLs, HyZU, vscDv, wWNm, xad, tuhtIn, GzsT, mnNuc, YseCxP, tioLCj, tliEaN, wikQ, sXnUL, hOi, wRX, IyavLc, qnYB, YndC, Chj, qDEFNO, tcx, rNTDh, jzCBR, DVjt, HGIAuv, LHAkIU, spR, VYlYq, hDPcnm, IMa, CKrWa, nrncmJ, uYBdHf, ISZTVd, esIHcn, Otpbzk, iIoJX, Hpim, oZPep, NYsw, eFTQ, HqCLV, NVoD, OvqwZ, AVgIXd, guXKfh, FjAGvA, lnOZ, AZpe, CnGo, OaeXQ, cKUxKN, NJAsCk, xpb, fuMfzy, QNQjDG, ywSrEM, MpS, fsN, XiM, JFEita, wZGK, Gvp, nvbkp, wRX, qwGjNc, xrf, jna, HXjQE, DGua, zCDko, NeP, YKbK, OamAc, byVf, HZdSw, gAe, SXc, osrz, JKrTt, qYaAIp, LKXtXw, xQVun, PNUE, hrwWW, sLgbuO, jBNb,

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