\n\n```\n\n```\n\n\n```\n\n\n(optional) If you need syntax highlighting, add the following script to include Prism and the Prism LaTeX stylesheet (or use any other):\n\n```\n\n\n\n```\n\n```\n\n\n\n```\n\n\n\nDone.\n\n## Class-based Elements\n\n### Author and Abstract\n\nUse the following code to add an author and abstract to your document. It will look like this.\n\n```\n

John Doe
December 7, 2020

\n\n\n```\n\n```\n

John Doe
December 7, 2020

\n\n\n```\n

John Doe
December 7, 2020

\n\n\n### Theorems, Definitions, Lemmas and Proofs\n\nTheorems, definitions, lemmas and proofs are supported. Just wrap your content in a div and add the corresponding class to the element like in the following example.\n\n```\n\n\n\n\n\n```\n\n```\n\n\n\n\n\n```\n\n\n\n\n\nBelow are some examples.\n\n#### Proofs & Theorems\n\nThe real numbers $\\mathbb{R}$ are uncountable.\n\nIf $\\mathbb{R}$ is countable, then [0, 1] is countable as well. Hence there exists a map C from $\\mathbb{N}$ onto [0, 1] with $$C(n)=\\sum_{i=1}^{\\infty} c_{i}(n) 10^{-i}$$ where $c_{i}(n) \\in\\{0,1, \\ldots, 9\\},$ are the digits in decimal expansion. Now consider a real number $$x=\\sum_{i=1}^{\\infty} \\bar{c}_{i} 10^{-i} \\in[0,1]$$ with $\\bar{c}_{i} \\neq c_{i}(i)$. Obviously $C(n) \\neq x$ for all $n \\in \\mathbb{N} .$ Hence $C$ is not onto. A contradiction.\n\nIf $S$ is both countable and infinite, then there is a bijection between $S$ and $\\boldsymbol{N}$ itself.1\n\nFor any $s \\in S,$ we let $f(s)$ denote the value of $k$ such that $s$ is the $k$ the smallest element of $S .$ This map is well defined for any $s,$ because there are only finitely many natural numbers between 1 and $s .$ It is impossible for two different elements of $S$ to both be the $k$ the smallest element of $S$. Hence $f$ is one-to-one. Also, since $S$ is infinite, $f$ is onto.\n\n#### Lemmas\n\nAn even number plus an even number results in an even number.\n\n#### Definitions\n\nA definition is a a statement of the meaning of a word or word group or a sign or symbol.2\n\n### Paragraphs\n\nIn order to get automatic first line indentation of paragraphs, like in default LaTeX articles, the class \n```\nindent-pars\n```\nindent-pars can be used with \n```\narticle\n```\narticle tag.\n\n```\n

\n ...\n

\n\n```\n\n```\n

\n ...\n

\n\n```\n

\n ...\n

\n\nThe CSS style provided follows \n```\nbabel\n```\nbabel specific language rules: by default, the first paragraph after a section title is not indented in English, unlike Spanish and French languages.\n\nTo avoid first line indentation of some specific paragraph, the class \n```\nno-indent\n```\nno-indent can be used.\n\n```\n

...

\n\n```\n\n```\n

...

\n\n```\n

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\n\n### Table Classes\n\n#### Custom Table Borders\n\nTo add custom borders to the table, you should use the class \n```\nborders-custom\n```\nborders-custom with \n```\n\n```\n tag, to begin with a table without any border. The classes \n```\nborder--thin\n```\nborder--thin and \n```\nborder--thick\n```\nborder--thick, are available, where \n```\n\n```\n can take one of the values: \n```\ntop\n```\ntop, \n```\nright\n```\nright, \n```\nbottom\n```\nbottom, \n```\nleft\n```\nleft.\n\n```\n\n \n \n \n \n \n \n ...\n\n```\n\n```\n

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...	...	...

\n \n \n \n \n \n \n ...\n\n```\n

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\n \n \n \n \n \n \n ...\n\nSee full examples in the section about tables.\n\n#### Table Column Alignment\n\nFor each column of the table, there is one class for left, center or right alignment, up to 12 columns: \n```\ncol--l\n```\ncol--l, \n```\ncol--c\n```\ncol--c, \n```\ncol--r\n```\ncol--r, \n```\nn\n```\nn=1, ...,12. For example, a table with 3 columns using the following classes\n\n```\n

...	...	...
...	...	...

\n \n \n \n ...\n\n```\n\n```\n

...

...

...

\n \n \n \n ...\n\n```\n

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\n \n \n \n ...\n\naligns the first column to the left, centers the second one and aligns the third to the right.\n\nSee full examples in the section about tables.\n\n## Language Support\n\nThe labels of theorems, definitions, lemmas and proofs can be changed to other supported language by including the following snippet, linking to the desired language in addition to the main CSS file.\n\n```\n\n ...\n\n\n```\n\n```\n\n ...\n\n\n```\n\n ...\n\n\nTake a peek at the language support demo to see how the labels of the different languages change.\n\n## Sidenotes\n\nSidenotes can be used as an alternative to footnotes, where the user does not have to jump to the bottom of the page to read it. On mobile, click the superscript to reveal the noteYay, sidenotes!. If you are on mobile, I will appear inline. If you are using a larger screen, the sidenote will appear to the right of the text..\n\nSidenotes do need a little bit of setup, they are made up of a label, an invisible checkbox on top of the number and a span with the text inside. The superscript is set automatically and incremented using CSS when the checkbox has a class of \n```\nsidenote-number\n```\nsidenote-number.\n\n```\n\n\n\n\n```\n\n```\n\n\n\n\n```\n\n\n\n\nIf you do not need superscripted numbers, you can opt out of the \n```\nsidenote-number\n```\nsidenote-number class and the sidenote will not have a number assigned. On a smaller screen, you will need to add a symbol inside the \n```\nlabel\n```\nlabel for the user to click on. ⊕This is a sidenote without a number.\n\nThe snippet for a sidenote without a number is very similar:\n\n```\n⊕\n\n\n\n```\n\n```\n⊕\n\n\n\n```\n⊕\n\n\n\nAdd a class of \n```\nleft\n```\nleft to the span with the \n```\nsidenote\n```\nsidenote class to make the note appear on the left side of the page on instead of right.\n\nThe symbol you could use to indicate a sidenote is up to you. What about this notebook. 📝A notebook indicating a note. Aha.\n(if on a large screen, resize to mobile to see the emoji)\n\n## Dark Mode\n\nThere is built-in support for dark mode. By default, the document is in light mode. To enable dark mode, add the \n```\nlatex-dark\n```\nlatex-dark class to the \n```\n\n```\n element. This will force the document to be in dark mode.\n\nIf you want enable dark mode based on the \n```\nprefers-color-scheme\n```\nprefers-color-scheme CSS media query, then use the \n```\nlatex-dark-auto\n```\nlatex-dark-auto class instead.\n\nYou can also add a dark mode toggle to your site by adding a button and a tiny bit of JavaScript:\n\n```\nToggle dark mode\n\n```\n\n```\nToggle dark mode\n\n```\nToggle dark mode\n\n```\ndocument\n .querySelector(\"#dark-mode-toggle\")\n .addEventListener('click', () => {\n document.body.classList.toggle(\"latex-dark\");\n });\n\n```\n\n```\ndocument\n .querySelector(\"#dark-mode-toggle\")\n .addEventListener('click', () => {\n document.body.classList.toggle(\"latex-dark\");\n });\n\n```\ndocument\n .querySelector(\"#dark-mode-toggle\")\n .addEventListener('click', () => {\n document.body.classList.toggle(\"latex-dark\");\n });\n\nLike this:\n\n## Alternative Typeface\n\nLaTeX.css uses Latin Modern by default. If you don't like this typeface (hard to read, too thin, etc.), you can switch to the \n```\nLibertinus\n```\nLibertinus font family by adding a class of \n```\nlibertinus\n```\nlibertinus to the \n```\n\n```\n tag. Click the button below to switch between Latin Modern and Libertinus.\n\n## HTML Elements\n\nFor a preview of all HTML elements with LaTeX.css, check out the HTML5 elements test page.\n\n### Text Formatting\n\nThis sentence is bold. If you like semantics, you might go with strong or emphasized text. If not, italic is still around. Small text is for fine print. Your copy can also be subscripted and superscripted, inserted, deleted, or highlighted. You would use a hyperlink to go to a new page. Keyboard input elements like Cmd + Shift are used to display textual user input.\n\n### Blockquotes\n\nGive me six hours to chop down a tree and I will spend the first four sharpening the axe. — Abraham Lincoln\n\n### Definition Lists\n\nDefinition Title One\n\nFirst definition description\n\nBinomial theorem\n\n$$(x+y)^{n}=\\sum_{k=0}^{n}\\left(\\begin{array}{l}n \\\\ k\\end{array}\\right) x^{n-k} y^{k}=\\sum_{k=0}^{n}\\left(\\begin{array}{l}n \\\\ k\\end{array}\\right) x^{k} y^{n-k}$$\n\n### Tables\n\nA sample table with a descriptive caption.\n\nHeader 1\n\nHeader 2\n\nHeader 3\n\nFooter 1\n\nFooter 2\n\nFooter 3\n\nDescription 1\n\nDescription 2\n\nDescription 3\n\nDescription 1\n\nDescription 2\n\nDescription 3\n\nDescription 1\n\nDescription 2\n\nDescription 3\n\nExample table taken from this paper on how to produce quality tables with LaTeX.\n\nItem\n\nAnimal\n\nDescription\n\nPrice ($)\n\nGnat\n\nper gram\n\n13.65\n\nGnu\n\nstuffed\n\n92.50\n\nEmu\n\nstuffed\n\n33.33\n\nArmadillo\n\nfrozen\n\n8.99\n\nExample table with custom borders and aligment.\n\nDe Morgan's Law: $\\lnot P \\lor \\lnot Q \\iff \\lnot (P \\land Q)$\n\nTRUTH TABLE\n\n$P$\n\n$Q$\n\n$\\lnot P$\n\n$\\lnot Q$\n\n$P \\land Q$\n\n$\\lnot P \\lor \\lnot Q$\n\n$\\lnot (P \\land Q)$\n\nT\n\nT\n\nF\n\nF\n\nT\n\nF\n\nF\n\nF\n\nT\n\nF\n\nT\n\nT\n\nF\n\nT\n\nT\n\nF\n\nF\n\nT\n\nT\n\nF\n\nT\n\nF\n\nT\n\nT\n\nClose approaches to the Earth by NEOs.\n\nCA Date\n\nObject Name\n\nDiameter\n\nDist. Min. (LD)\n\n2023-Jul-10\n\n2018 NW\n\n7.3m-16m\n\n0.287\n\n2023-Jul-10\n\n2023 LN1\n\n45m-00m\n\n17.813\n\n2023-Jul-11\n\n2023 MD2\n\n36m-80m\n\n5.570\n\n2023-Jul-11\n\n2023 NE\n\n32m-70m\n\n11.253\n\n2023-Jul-11\n\n2023 MQ1\n\n28m-62m\n\n10.716\n\n2023-Jul-12\n\n2023 OM\n\n20m-46m\n\n7.628\n\n2023-Jul-12\n\n2018 UY\n\n190m-420m\n\n7.412\n\n### Images\n\nMountain landscape by John Towner.\n\n## Miscellaneous\n\n### Scroll Overflow\n\nIt is best to break up long equations into smaller parts, but when this isn't possible, consider wrapping the overflowing element with a class of \n```\nscroll-wrapper\n```\nscroll-wrapper to allow scrolling on the x-axis. Large tables should also be wrapped with this class.\n\nBelow is an example of a long equation with overflow scroll.\n\n$$(1+x)^{n}=1+n x+\\frac{n(n-1)}{2 !} x^{2}+\\frac{n(n-1)(n-2)}{3 !} x^{3}+\\frac{n(n-1)(n-2)(n-3)}{4 !} x^{4}+\\frac{n(n-1)(n-2)(n-3)(n-4)}{5 !} x^{5}+\\ldots$$\n\n### Syntax Highlighting\n\nIf you need syntax highlighting for code, LaTeX.css provides a PrismJS theme that immitates the minted package for LaTeX. Add the following stylesheet and script:\n\n```\n\n\n\n```\n\n```\n\n\n\n```\n\n\n\nAnd use it like this:\n\n```\n

\n \n \n \n

\n\n```\n\n```\n

\n \n \n \n

\n\n```\n

\n \n \n \n

\n\nChange which languages Prism highlights by customising the script here.","prompt_model":"gpt-4o-mini","image_prompt_model":"replicate:black-forest-labs/flux-schnell","image_prompt_name":"GenerateGameArt-v1","image_prompt_text":"cyberpunk cityscape, neon lights reflecting on rain-soaked streets, a figure in a dark hoodie surrounded by holographic interfaces, digital codes and binary streams floating in the air, whimsical AI avatars popping up with quirky expressions, shadowy silhouettes of towering corporate buildings silhouetted against a dusk sky, tension-filled atmosphere with a glowing countdown timer, vibrant yellow (#FFCC00) accents illuminating the scene, swirling data streams, dramatic contrasts between dark and bright tech elements, inspired by artists like Syd Mead and Katsuhiro Otomo, dynamic composition, 4k, hd, digital art, cinematic lighting, energetic ambiance, retro-futuristic vibes","image_data":null,"music_prompt_text":null,"music_prompt_seed_image":null,"private":false,"createdAt":"2024-12-02T18:09:51.653Z","updatedAt":"2024-12-02T18:15:18.032Z","UserId":null}, { parent_id: window.ia.params.parent_id, chat_id: window.ia.params.chat_id, action: window.ia.params.action, }); window.ia.handleRadio(33084); window.history.pushState({}, document.title, window.location.pathname); });

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