double vertical bar in math
This is a legacy of keyboards manufactured during the 1980s and 1990s for IBM PC compatible computers featuring the broken bar, as such computers used IBM's 8-bit Code page 437 character set based on ASCII, which continued to display the glyph for the broken bar at codepoint 7C on displays from MDA (1981) to VGA (1987) despite the changes made to ASCII in 1977. In JavaScript for example, we use the pipe character like this: You might be wondering how to type the vertical line (pipe character) on your keyboard. !, which, outside string literals, is equivalent to the | character. Another way to type the vertical bar character is to turn on the numeric keypad, hold ALT, then press 1, 2, and 4. Use MathJax to format equations. Received a 'behavior reminder' from manager. Note: These symbols use combining characters and may not appear correctly in some older browsers. HTML symbol, character and entity codes, ASCII, CSS and HEX values for Double Vertical Bar Double Right Turnstile, plus a panoply of others. c The article defines this equation as: The gap impedance, or the impedance looking to the right from the right-most terminal of X1 is: What do the double vertical bars mean in this context? To learn more, see our tips on writing great answers. Connect and share knowledge within a single location that is structured and easy to search. I hope to get something like D(S||Q) where S=||P||/2. Use MathJax to format equations. It can be defined as. The vertical bar is used as a special character in lightweight markup languages, notably MediaWiki's Wikitext (in the templates and internal links). What does an Impedance of a transformer mean? This includes many German QWERTZ keyboards. Connect and share knowledge within a single location that is structured and easy to search. Using just \| instead of \right| \left| for the middle double bar results in a short middle double bar. How could my characters be tricked into thinking they are on Mars? Plastics are denser than water, how comes they don't sink! HTML Arrows offers all the html symbol codes you This may have been to distinguish the character from the lower-case 'L' and the upper-case 'I' on these limited-resolution devices, and to make a vertical line of them look more like a horizontal line of dashes. Does anyone has a good idea on how to achieve that. 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. I want to be able to quit Finder but can't edit Finder's Info.plist after disabling SIP. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked, Counterexamples to differentiation under integral sign, revisited, Bracers of armor Vs incorporeal touch attack. The simplest way to cope with the problem is to use mathtools facilities: Note that number 1 is wrong in two respects: there is an unwanted space between the "D" and the left parenthesis; the two bars are too near the symbols, making for ambiguity. Programmers also call this character the pipe symbol. Some codes like that for x (X-bar) are actually a combination of two codes the base letter x plus a code for the line above (̄: or ). So, to type it, you have to hold SHIFT, then press the backslash key: Another way to type the vertical bar character is to turn on the numeric keypad, hold ALT, then press 1, 2, and 4. We'd like to keep answers separate from questions, so you should write a separate answer instead of editing your answer into the question. Why is the first bar missing in my second plot in pgsplots when I set `axis lines=left`? Now you know how to type the vertical line or pipe character on your keyboard, and you can use it in your math or programming tasks. Some variants of EBCDIC included both versions of the character as different code points. In other words, if you have an X resistor in parallel with a Y resistor, the equivalent resistance of the two will be X | | Y . Else, I could just create a new notation. In MathJax use $lVert$ and $rVert$. X | | Y 1 1 X + 1 Y. Although not as common as commas or tabs, the vertical bar can be used as a delimiter in a flat file. Are there any packages to import bibxml into (la)tex? Not the same as \[LeftDoubleBracketingBar], \[RightDoubleBracketingBar]. [8] This draft received opposition from the IBM user group SHARE, with its chairman, H. W. Nelson, writing a letter to the American Standards Association titled "The Proposed revised American Standard Code for Information Interchange does NOT meet the needs of computer programmers! I've searched the Comprehensive LATEX Symbol List but failed to find anything conclusive in there. Examples: A pipe is an inter-process communication mechanism originating in Unix, which directs the output (standard out and, optionally, standard error) of one process to the input (standard in) of another. Since you mention using a vertical bar as a binary relation, you may want $\mid$ which is kerned to sit midway between its neighbours. I managed to find out how to do it with this useful operator middle. Self-answers are perfectly admissible, and a well-written answer may earn you additional reputation. But that has no double-bar version so finally, you have the option of $\mathrel{\Vert}$ which is both double-bar and kerned to the centre. Should teachers encourage good students to help weaker ones? An alternative is to use \Big\| . And instead of \Big one can use \big or \bigg , etc. depending on how much length you want. 2. How to repair freezing video, vertical bar, and double image. In many programming languages, the vertical bar is used to designate the logic operation or, either bitwise or or logical or. I've found this discussion, in which Stefan and Thorsten propose the alternatives below. What aspect of what I put is untrue? \middle \vert. {\displaystyle a|b\|c} I tried. Updated on September 08, 2020. http://web.mit.edu/6.685/www/chapter8.pdf. I managed to find out how to do it with this useful operator \middle. On a Mac, to enter the Double Vertical Bar symbol: Command + Control + Spacebar shortcut to open the Character Viewer. We accomplish this by creating thousands of videos, articles, and interactive coding lessons - all freely available to the public. Why does the distance from light to subject affect exposure (inverse square law) while from subject to lens does not? I want to use the double-bar notation for second-order tensors, which is common in continuum mechanics (e.g. In regular expression syntax, the vertical bar again indicates logical or (alternation). Compare set-builder notation. Many early video terminals and dot-matrix printers rendered the vertical bar character as the allograph broken bar . This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. The numbers suit cm and lm fonts, for other fonts they might need to be modified. It is located right above the Enter key. However, this makes the bar unusable as the regular expression "alternative" operator. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It can be defined as, $$X\ ||\ Y \triangleq\frac{1}{\frac{1}{X}+\frac{1}{Y}}$$. 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. I hope to get something like D(S||Q) where S=||P||/2. rev2022.12.9.43105. Which, when we apply the table above between each binary digit of the two numbers: 0 or 0 = 0 0 or 0 = 0 0 or 0 = 0 0 or 1 = 1. give us 0001, which when converted to decimal becomes 1. The broad implementation of the extended ASCII ISO/IEC 8859 series in the 1990s also made a distinction between the two forms. How to suppress table numbering for 1 table Latex. Thanks In the Geneva Bible and early printings of the King James Version, a double vertical bar is used to mark margin notes that contain an alternative translation from the original text. Does anyone has a good idea on how to achieve that. The broken bar character can be typed (depending on the layout) as .mw-parser-output .keyboard-key{border:1px solid #aaa;border-radius:0.2em;box-shadow:0.1em 0.1em 0.2em rgba(0,0,0,0.1);background-color:#f9f9f9;background-image:linear-gradient(to bottom,#eee,#f9f9f9,#eee);color:#000;padding:0.1em 0.3em;font-family:inherit;font-size:0.85em}AltGr+` or AltGr+6 or AltGr+ Shift+Right \ on Windows and Compose!^ on Linux. How many transistors at minimum do you need to build a general-purpose computer? The vertical bar is used in braket notation in quantum physics. 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. HSpice Manuals/Handbooks. You'll use it in mathematics and programming, in Linux, and in computer science fields to represent different things. Why is this usage of "I've to work" so awkward? Undefined control sequence." Female OP protagonist, magic. Unicode. A common notation used for information divergence is D(P||Q). Help us identify new roles for community members, What does negative impedance mean in the context of miller's theorem. Share. Update When would I give a checkpoint to my D&D party that they can return to if they die? Donations to freeCodeCamp go toward our education initiatives, and help pay for servers, services, and staff. MathJax reference. Are the S&P 500 and Dow Jones Industrial Average securities? By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The alias for \[DoubleVerticalBar] has a space at the beginning. Sed based on 2 words, then replace whole line with variable, Penrose diagram of hypothetical astrophysical white hole. In music, when writing chord sheets, single vertical bars associated with a colon (|: A / / /:|) represents the beginning and end of a section (e.g. [citation needed]. In this way, a series of commands can be "piped" together, giving users the ability to quickly perform complex multi-stage processing from the command line or as part of a Unix shell script ("bash file"). Other Word Forms Noun Singular: vertical-bar. In later printings of the King James Version, the double vertical bar is irregularly used to mark any comment in the margins. The pipe character is not hidden on a keyboard. Why is the WWF pending games (Your turn) area replaced w/ a column of Bonus & Rewardgift boxes. In Sanskrit and other Indian languages, a single vertical mark, a danda, has a similar function as a period (full stop). It is also traditionally used to mark the division between lines of verse printed as prose (the style preferred by Oxford University Press), though it is now often replaced by the forward slash. ). Since you mention using a vertical bar as a binary relation, you may want $mid$ which is kerned to sit midway between its neighbours. This is standard notation in electrical engineering, used for parallel impedances. Now you know how to type the vertical line or pipe character Steel, June 8, 1966, Honeywell Inc. X3.2 Standards Subcommittee Records, 1961-1969 (CBI 67), Charles Babbage Institute, University of Minnesota, Minneapolis, box 1, folder 23. Making statements based on opinion; back them up with references or personal experience. The simplest way to cope with the problem is to use mathtools facilities: I tried. The double bar symbol | is used to denote certain kinds of norms in mathematics (e.g., ||x|| or ||x||_2). 0. What is the meaning of || (double vertical bar) in this KL divergence equation? The danda has its own Unicode code point, U+0964. Note that number 1 is wrong in two respects: there is an unwanted space between the "D" and the left parenthesis; the two bars are too near the symbols, making for ambiguity. In MathJax use $\lVert$ and $\rVert$ . The capital v gives you double bars while the lower case v in $\lvert$ gives you single vertical bars. 1. @campa thanks, you may be right because I don't fully understand your comment. I tried. You can make a tax-deductible donation here. 28. A double vertical bar is used to write the alveolar lateral click (). There are many types of norms you can define, which all follow basic rules. Thats what Im going to show you in this article. Try you construction as part of the text, using. I wonder if it is possible to display it nicely ? For example: the Unix command grep -E 'fu|bar' matches lines containing 'fu' or 'bar'. How to correctly align the uncertainty symbols in this table, and control horizontal column alignment? It is frequently used because vertical bars are typically uncommon in the data itself. Unicode. The most common norm is the euclidean norm in euclidean space. What does this gated recurrent unit notation mean? math.stackexchange.com/questions/1597380/, Help us identify new roles for community members. do you know anybody i could submit the designs too that could manufacture the concept and put it to use, Need help finding a book. The double vertical bar operator "||" denotes string concatenation in PL/I, standard ANSI SQL, and theoretical computer science (particularly cryptography). Define vertical-bar. This overlaps three things: wedge/vee, shortmid, and shortmid raised to a correct height. That is, [ba] covers the pronunciations [ba] and [ba].[15]. How to smoothen the round border of a created buffer to make it look more natural? [13][failed verification] The broken bar does not appear to have any clearly identified uses distinct from those of the vertical bar. X | | Y 1 1 X + 1 Y. Else, I could just create a new notation. Just read as KL divergence between $Q(z)$ and $P(z|X)$. Typesetting the following math formulas with kpfonts \documentclass{article} \usepackage{kpfonts-otf} \begin{document} $\left.g\right\vert, \left.g\right\Vert$ \end{document} produces a vertical bar that does not go sufficiently low to cover the descender of g. By contrast, the double vertical bar goes low enough. But it's not clear to me what to you is the "right" height. (TA) Is it appropriate to ignore emails from a student asking obvious questions? Since these are technically letters, they have their own Unicode code points in the Latin Extended-B range: U+01C0 for the single bar and U+01C1 for the double bar. Changing the bibliography heading style with `apacite` and the `letter` document style, unicode-math superscripts dont line up (using XeLaTeX), Change font of bibliography content not Heading, chemfig: bonds shifting downward after subscripts, Reproduce animation from PowerPoint with LaTeX. Similarly, the vertical bar may see use as a delimiter for regular expression operations (e.g. What does mean in the equations? Copy Hex ⊫ Copy HTML ⊫ Copy Entity [9] As a compromise, a requirement was introduced where the exclamation mark (!) The \textbar command can be used to produce a vertical bar. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. b did anything serious ever run on the speccy? Tweet a thanks, Learn to code for free. and circumflex (^) would display as logical OR (|) and logical NOT () respectively in use cases such as programming, while outside of these use cases they would represent their original typographic symbols: It may be desirable to employ distinctive styling to facilitate their use for specific purposes as, for example, to stylize the graphics in code positions 2/1 and 5/14 to those frequently associated with logical OR (|) and logical NOT () respectively. To learn more, see our tips on writing great answers. Used in geometry to mean parallel to . IUPAC nomenclature for many multiple bonds in an organic compound molecule. X3.2 document X3.2/475, December 13, 1966, Honeywell Inc. X3.2 Standards Subcommittee Records, 1961-1969 (CBI 67), Charles Babbage Institute, University of Minnesota, Minneapolis, box 1, folder 22. International Phonetic Alphabet Brackets and transcription delimiters, "7-bit character sets: Revisions of ASCII", "Character histories - notes on some Ascii code positions", "ASCII Chart: IBM PC Extended ASCII Display Characters", "Detailed descriptions of the characters", https://en.wikipedia.org/w/index.php?title=Vertical_bar&oldid=1125218268, Short description is different from Wikidata, Articles containing Russian-language text, Articles with unsourced statements from May 2020, Articles with failed verification from July 2020, Creative Commons Attribution-ShareAlike License 3.0, A vertical bar can be used to separate variables from fixed parameters in a function, for example, This page was last edited on 2 December 2022, at 20:53. Since you mention using a vertical bar as a binary relation, you may want $mid$ which is kerned to sit midway between its neighbours. I tried $D \left( \frac{\|P\|}{2} \right| \left| Q \right)$ The above do not work as the middle bar are not of the same vertical height Not sure if it was just me or something she sent to the whole team, 1980s short story - disease of self absorption. This is useful when the regular expression contains instances of the more common forward slash (/) delimiter; using a vertical bar eliminates the need to escape all instances of the forward slash. I hope to get something like D(S||Q) where S=||P||/2. Texworks crash when compiling or "LaTeX Error: Command \bfseries invalid in math mode" after attempting to, Error on tabular; "Something's wrong--perhaps a missing \item." In such a way that the middle double bar has the right height. 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 is used as a mathematical symbol in numerous ways: The double vertical bar, To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Typically the symbol is used in an expression like this: 3. a 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. a Show that this simple map is an isomorphism. [11][12] However, the 1977 revision (ANSI X.3-1977) undid the changes made in the 1967 revision, enforcing that the circumflex could no longer be stylised as a logical NOT symbol, the exclamation mark likewise no longer allowing stylisation as a vertical bar, and defining the code point originally set to the broken bar as a solid vertical bar instead;[11] the same changes were also reverted in ISO 646-1973 published four years prior. This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. Prove: For a,b,c positive integers, ac divides bc if and only if a divides b. Copy Hex ⊯ Copy HTML ⊯ Copy Longer single and double vertical bars are used to mark prosodic boundaries in the IPA. Double Vertical Bar Double Right Turnstile: Symbol: : Unicode Number: U+022AB: HTML Code: ⊫ HTML Entity: ⊫ CSS Code: \22AB: UTF-8 Encoding: 0x22AB: UTF-16 This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. The simplest way to cope w Is Energy "equal" to the curvature of Space-Time? How to plot the graph of sine and its inverse function in same coordinates? PROCEDURE. Also I started out thinking of $\mid$ and then changed when I realsed there is no $\Mid$. @jhin Not necessarily. U+022AF. Double Vertical Bar Double Right Turnstile () . The simplest way to cope with the problem is to use mathtools facilities: Note that number 1 is wrong in two respects: there is an unwanted space between the "D" and the left parenthesis; the two bars are too near the symbols, making for ambiguity. How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5, Ive designed a space elevator using a series of lasers. This has different spacing from \mid and \parallel, which are relational operators: a \mid b \parallel c is set as Debian/Ubuntu - Is there a man page listing all the version codenames/numbers? , is also employed in mathematics. in sed). The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. Copy Hex ⊫ Copy HTML ⊫ Copy Entity We also have thousands of freeCodeCamp study groups around the world. The pipe in APL is the modulo or residue function between two operands and the absolute value function next to one operand. The vertical bar symbol is used in math to represent the absolute value operator. [14] In non-computing usefor example in mathematics, physics and general typographythe broken bar is not an acceptable substitute for the vertical bar. b for the strain and stress tensors). It signifies the "norm" of the vector. But it's not clear to me what to you is the "right" height. We use the vertical line character, |, in various scenarios and contexts. math-mode. IF so I will prune these comments. 54,254 Solution 1. It only takes a minute to sign up. Meaning of vertical bar | in loss function? U+022AB. (No itemize or enumerate), "! || is the alias for \[Or]. In MathJax use $\lVert$ and $\rVert$. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. \end{document}, TEXMAKER when compiling gives me error misplaced alignment, "Misplaced \omit" error in automatically generated table. The length of How to add Double Vertical Bar Double Right Turnstile in CSS? Our mission: to help people learn to code for free. See page 60 and table 3.8 of the Not so short intro. {\displaystyle \|} [8] A subsequent draft on May 12, 1966, places the vertical bar in column 7 alongside regional entry codepoints, and formed the basis for the original draft proposal used by the International Standards Organisation. The reminder is perhaps helpful because KL is used much like a distance, but it's not symmetric, so it's not a distance. Asking for help, clarification, or responding to other answers. Two bars || (a 'double danda') is the equivalent of a pilcrow in marking the end of a stanza, paragraph or section. freeCodeCamp's open source curriculum has helped more than 40,000 people get jobs as developers. Add a new light switch in line with another switch? The capital v gives you double bars while the lower case v in $lvert$ gives you single vertical bars. The best answers are voted up and rise to the top, Not the answer you're looking for? It can be inserted into HTML as ¦ In some dictionaries, the broken bar is used to mark stress that may be either primary or secondary. Correctly formulate Figure caption: refer the reader to the web version of the paper? In LaTeX mathematical mode, the ASCII vertical bar produces a vertical line, and \| creates a double vertical line (a | b \| c is set as An initial draft for a 7-bit character set that was published by the X3.2 subcommittee for Coded Character Sets and Data Format on June 8, 1961, was the first to include the vertical bar in a standard set. What is the meaning of $\|a\|_p=\left(\sum _{i=1}^n \left|a_i(t)\right|{}^p\right){}^{\frac{1}{p}}$? This is standard notation in electrical engineering, used for parallel impedances. "; in this letter, he argues that no characters within the international subset designated at columns 2-5 of the character set would be able to adequately represent logical OR and logical NOT in languages such as IBM's PL/I universally on all platforms. Conduct a review on constructing single vertical and horizontal bar graphs (TG p. 337) Establishing a purpose for the lesson. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Using just | instead of right| left| for the middle double bar results in a short middle double bar. The rubber protection cover does not pass through the hole in the rim. In BackusNaur form, an expression consists of sequences of symbols and/or sequences separated by '|', indicating a choice, the whole being a possible substitution for the symbol on the left. What does the double vertical bar mean here? File ended while scanning use of \@imakebox. In most Unix shells (command interpreters), this is represented by the vertical bar character. For example A || C. In Linux, you can use it to combine commands you want to execute all together. The same "pipe" feature is also found in later versions of DOS and Microsoft Windows. Double vertical bars enclosing an object is the norm of the object. Thus 0|1 is: 0000 | 0001. Get started, freeCodeCamp is a donor-supported tax-exempt 501(c)(3) nonprofit organization (United States Federal Tax Identification Number: 82-0779546). A small bolt/nut came off my mtn bike while washing it, can someone help me identify it? X-Bar, P-Hat and D-Bar. This might be wrong. But that has no double-bar version so U+022AB. The HTML Entity for Double-Vertical-Bar-Double-Right-Turnstile is ⊫. Thanks for contributing an answer to Cross Validated! I haven't been able to find it from googling. 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. 2 Author by MegaNightdude. I managed to find out how to do it with this useful operator \middle, Bars, bar lines, double bar lines, repeat signs, 1st and 2nd time bars, da capo, coda, How To Type Parallel To Symbol in Word: How Insert Double Vertical Line in Word, I'd rather recommend not using auto scaling unless it is absolutely necessary. Thanks Some fonts draw the characters the same (both are solid vertical bars, or both are broken vertical bars). You can also use the HTML Code (, CSS Code (22AB), Hex Code (), or Unicode (22AB) to insert the symbol for Double-Vertical-Bar-Double-Right-Turnstile. Negated Double Vertical Bar Double Right Turnstile () . [citation needed] Single bars can also represent the beginning and end of measures (|: A / / / | D / / / | E / / /:|). In Mathematics, the double pipe (||) signifies that one line is parallel to the other. But that has no double-bar version so finally, you have the option of $mathrel{Vert}$ which is both double-bar and kerned to the centre. Comments. I wonder if it is possible to display it nicely ? DC Analysis of Transistor Circuits - Double vertical line symbol. Web developer and technical writer focusing on frontend technologies. I've also tried \bigg\rvert with no luck. Else, I could just create a new notation. Answered by samerivertwice on April 5, 2021, superscripts unicode math vertical alignment xetex, 2022 AnswerBun.com. Constructing Double Vertical Bar Graph (MATH 4 QUARTER 4) SirJon - TV. 'little stick'), indicating the preceding consonant is an ejective. If a particular protein contains 178 amino acids, and there are 367 nucleotides that make up the introns in this gene. What does \$x^*(t)=x(t)\$ mean in signals and systems? TeX - LaTeX Asked by shunjie on April 5, 2021, A common notation used for information divergence is D(P||Q). Statistics Symbols using Combining Diacritics. What does line impedance stabilization mean? Is there any reason on passenger airliners not to have a physical lock between throttles? Step 2: Sort the collected data as per the category. Did neanderthals need vitamin C from the diet? This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. -- Update -- It mostly depends on what D represents. MathJax reference. to LaTeX for further details. What does a High Impedance input mean for an ADC. The vertical bar is also used in regular expressions to specify alternative Thanks CGAC2022 Day 10: Help Santa sort presents! Create a table to build the bar graph. Closed 6 years ago. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir, Is there any way to make nopagebreak work before paracol. Activity cards, sample double horizontal and vertical bar graphs. A double vertical bar || or is the standard caesura mark in English literary criticism and analysis. Using just \| instead of \right| \left| for the middle double bar results in a short middle double bar. It only takes a minute to sign up. Why is the federal judiciary of the United States divided into circuits? It's from page 8 of https://arxiv.org/pdf/1606.05908.pdf. Dictionary Thesaurus Sentences Examples (mathematics) Set definitions (e.g.) Based on what you posted, they are using it to refer to the "Euclidean Norm" which is, as the comments suggest, the "length" of the vectors here. This double bar should be treated as a binary relation, so it will be distinguishable from other usages, such as a norm. It can be defined as. In other words, if you have an X resistor in parallel Leboy Technician. Unicode. Double Vertical Bar Double Right Turnstile () . Larus Thorlacius, Thordur Jonsson (eds.). Does integrating PDOS give total charge of a system? Intro, Interlude, Verse, Chorus) of music. The reminder is perhaps helpful because KL is used much like a distance, but it's not It is also used to denote parallel lines, as in AB, and in an Specifically, in C and other languages following C syntax conventions, such as C++, Perl, Java and C#, a | b denotes a bitwise or; whereas a double vertical bar a || b denotes a (short-circuited) logical or. Though, in this particular case I'd actually think that \Bigl [ a \Bigm \vert
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