[{"data":1,"prerenderedAt":192},["ShallowReactive",2],{"public-page:\u002Fen\u002Fmathjax-teru-nusqaulygy:en":3},{"id":4,"slug":5,"title":6,"content":7,"content_blocks":8,"media_by_id":181,"render_mode":182,"use_mathjax":183,"meta_defaults":184,"published_at":185,"updated_at":186,"article_author_name":187,"requested_lang":188,"resolved_lang":188,"available_langs":189,"localization_langs":189},"a14f5203-17f7-4605-b092-0fd4301c9d19","mathjax-teru-nusqaulygy","MathJax usage guide","@post_type: article\n@slug: mathjax-teru-nusqaulygy\n@topic_code: MATHJAX_GUIDE\n@title: MathJax usage guide\n@summary: A practical guide to writing mathematical formulas on QazMath with TeX\u002FLaTeX syntax.\n@author: QazMath редакциясы\n@source_label: QazMath; MathJax Documentation\n@source_url: https:\u002F\u002Fdocs.mathjax.org\u002Fen\u002Fstable\u002Finput\u002Ftex\u002Fmacros\u002F\n@tags: mathjax, latex, tex, formula\n@published_at: 2024-01-02T21:58:22+05:00\n\n@layout: 12\nc1 text: MathJax usage guide | style: heading\nc1 text: \"\"\" | style: paragraph\nMathJax displays mathematical formulas written with TeX\u002FLaTeX syntax on web pages. The examples below follow the MathJax configuration used by QazMath.\n\"\"\"\n---\n@layout: 12\nc1 text: 1. Inline and displayed formulas | style: subheading\nc1 text: \"\"\" | style: paragraph\nEnclose an inline formula in `\\$ ... \\$`. For example, `\\$\\sum_{i=0}^n i^2=\\frac{n(n+1)(2n+1)}{6}\\$` produces $\\sum_{i=0}^n i^2=\\frac{n(n+1)(2n+1)}{6}$.\n\nUse `\\$\\$ ... \\$\\$` to place a formula on a separate line. The `\\$ ... \\$` delimiters are explicitly enabled in QazMath; they are not enabled in MathJax by default.\n\"\"\"\n---\n@layout: 12\nc1 text: 2. Greek letters | style: subheading\nc1 text: \"\"\" | style: paragraph\nLowercase letters: `\\alpha` — $\\alpha$, `\\beta` — $\\beta$, `\\gamma` — $\\gamma$, `\\epsilon` — $\\epsilon$, `\\varepsilon` — $\\varepsilon$, `\\phi` — $\\phi$, `\\varphi` — $\\varphi$, `\\omega` — $\\omega$.\n\nUppercase letters: `\\Gamma` — $\\Gamma$, `\\Delta` — $\\Delta$, `\\Theta` — $\\Theta$, `\\Lambda` — $\\Lambda$, `\\Pi` — $\\Pi$, `\\Omega` — $\\Omega$.\n\"\"\"\n---\n@layout: 12\nc1 text: 3. Superscripts and subscripts | style: subheading\nc1 text: \"\"\" | style: paragraph\nUse `^` for a superscript and `_` for a subscript. Examples: `x_i^2` — $x_i^2$, `\\log_2 x` — $\\log_2 x$, `a_{n+1}` — $a_{n+1}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 4. Grouping expressions | style: subheading\nc1 text: \"\"\" | style: paragraph\nPlace several characters inside braces when they should form one superscript or subscript. In `10^10`, the superscript applies only to the first `1`; the correct form is `10^{10}`: $10^{10}$.\n\nWrite nested powers as `{x^y}^z` — ${x^y}^z$ or `x^{y^z}` — $x^{y^z}$. Other examples: `x_{i^2}` — $x_{i^2}$, `{x_i}^2` — ${x_i}^2$.\n\"\"\"\n---\n@layout: 12\nc1 text: 5. Delimiters and brackets | style: subheading\nc1 text: \"\"\" | style: paragraph\nOrdinary brackets can be typed directly: `(2+3)[4+4]` — $(2+3)[4+4]$. Their size, however, does not change to match the enclosed expression.\n\nUse `\\left` and `\\right` when brackets need to fit a large expression: $\\left(\\frac{\\frac{x+5}{x-3}}{x^2+5}\\right)$.\n\nThe same approach works for an absolute value, `\\left|x\\right|` — $\\left|x\\right|$, and braces, `\\left\\{x+1\\right\\}` — $\\left\\{x+1\\right\\}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 6. Fractions | style: subheading\nc1 text: \"\"\" | style: paragraph\nWrite a fraction as `\\frac{a+1}{b+1}`: $\\frac{a+1}{b+1}$. If nested fractions look too small in inline text, use `\\dfrac`: $\\dfrac{\\dfrac{\\dfrac{x+5}{x^3}}{x-3}}{x^2+5}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 7. Roots | style: subheading\nc1 text: \"\"\" | style: paragraph\nWrite a square root as `\\sqrt{x^3}`: $\\sqrt{x^3}$. For a cube root or an $n$th root, put the degree in square brackets: `\\sqrt[3]{\\frac{x}{y}}` — $\\sqrt[3]{\\frac{x}{y}}$, `\\sqrt[n]{a}` — $\\sqrt[n]{a}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 8. Functions and limits | style: subheading\nc1 text: \"\"\" | style: paragraph\nPut a backslash before a standard function name so that it appears upright and has the correct spacing before its argument: `\\sin x` — $\\sin x$, while `sin x` — $sin x$.\n\nCommon commands include `\\cos`, `\\tan`, `\\cot`, `\\log`, `\\ln`, `\\max`, `\\min`, and `\\sum`. Limit example: `\\lim_{x\\to 0}\\frac{\\sin x}{x}=1` — $\\lim_{x\\to 0}\\frac{\\sin x}{x}=1$.\n\"\"\"\n---\n@layout: 12\nc1 text: 9. Common symbols | style: subheading\nc1 text: \"\"\" | style: paragraph\n`\\lt \\gt \\le \\ge \\neq` — $\\lt\\; \\gt\\; \\le\\; \\ge\\; \\neq$\n`\\times \\div \\pm \\mp \\cdot` — $\\times\\; \\div\\; \\pm\\; \\mp\\; \\cdot$\n`\\cup \\cap \\setminus \\subset \\subseteq \\supset \\in \\notin \\varnothing` — $\\cup\\; \\cap\\; \\setminus\\; \\subset\\; \\subseteq\\; \\supset\\; \\in\\; \\notin\\; \\varnothing$\n`\\binom{n+1}{2k}` — $\\binom{n+1}{2k}$\n`\\to \\gets \\Rightarrow \\Leftarrow \\mapsto \\implies \\iff` — $\\to\\; \\gets\\; \\Rightarrow\\; \\Leftarrow\\; \\mapsto\\; \\implies\\; \\iff$\n`\\land \\lor \\lnot \\forall \\exists \\top \\bot \\vdash \\vDash` — $\\land\\; \\lor\\; \\lnot\\; \\forall\\; \\exists\\; \\top\\; \\bot\\; \\vdash\\; \\vDash$\n`\\star \\ast \\oplus \\circ \\bullet \\infty` — $\\star\\; \\ast\\; \\oplus\\; \\circ\\; \\bullet\\; \\infty$\n`90^\\circ` — $90^\\circ$\n`\\approx \\sim \\simeq \\cong \\equiv` — $\\approx\\; \\sim\\; \\simeq\\; \\cong\\; \\equiv$\n`\\dots \\cdots` — $a_1,a_2,\\dots,a_n$ and $a_1+a_2+\\cdots+a_{80}$\n\"\"\"\n---\n@layout: 12\nc1 text: 10. Spacing in formulas | style: subheading\nc1 text: \"\"\" | style: paragraph\nMost ordinary spaces inside a formula are ignored. Use `\\,`, `\\;`, `\\quad`, and `\\qquad` to add specific amounts of space: `a\\,b \\quad a\\;b \\qquad a b` — $a\\,b \\quad a\\;b \\qquad a b$.\n\"\"\"\n---\n@layout: 12\nc1 text: 11. Systems of equations and matrices | style: subheading\nc1 text: \"\"\" | style: paragraph\nUse `\\\\` to separate rows and `&` to separate or align columns.\n\nSystem of equations: `\\begin{cases} x+y=5 \\\\ x-y=1 \\end{cases}` — $\\begin{cases}x+y=5\\\\x-y=1\\end{cases}$.\n\nMatrix: `\\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix}` — $\\begin{pmatrix}1&2\\\\3&4\\end{pmatrix}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 12. Text and notation inside formulas | style: subheading\nc1 text: \"\"\" | style: paragraph\nUse `\\text{...}` to place ordinary text inside a formula: `x>0\\text{ when}` — $x>0\\text{ when}$.\n\nSegments, vectors, and other notation: `\\overline{AB}` — $\\overline{AB}$, `\\vec{a}` — $\\vec{a}$, `\\hat{x}` — $\\hat{x}$, `x\\in\\mathbb{R}` — $x\\in\\mathbb{R}$.\n\"\"\"\n---\n@layout: 12\nc1 text: 13. Common mistakes | style: subheading\nc1 text: \"\"\" | style: paragraph\n• Always close an opening formula delimiter: `\\$...\\$` or `\\$\\$...\\$\\$`.\n• Put a multi-character superscript, subscript, or argument inside `{...}`.\n• Do not omit the `\\` before a command name: `\\sin`, `\\sqrt`, `\\frac`.\n• Write an ordinary dollar sign in text as `\\$` so that it is not treated as the start of a formula.\n\"\"\"\n---\n@layout: 12\nc1 text: Further reference | style: subheading\nc1 text: \"\"\" | style: paragraph\nComplete command list: https:\u002F\u002Fdocs.mathjax.org\u002Fen\u002Fstable\u002Finput\u002Ftex\u002Fmacros\u002F\n\nShort practical examples: https:\u002F\u002Fmath.meta.stackexchange.com\u002Fquestions\u002F5020\u002Fmathjax-basic-tutorial-and-quick-reference\n\"\"\"\n---\n@layout: 12\nc1 text: Conclusion | style: subheading\nc1 text: \"\"\" | style: paragraph\nYou can practise typing formulas in the comments section. To make a question about a problem or a reported error clear to everyone, write formulas in MathJax format.\n\nExample: `The equation of line \\$AB\\$ is \\$2x+3y=7\\$. Also, \\$\\sin^2 x+\\cos^2 x=1\\$.`\n\"\"\"",[9,25,37,49,61,73,85,97,109,121,133,145,157,169],{"id":10,"columns":11},"row-1794121050506-e6a387",[12],{"id":13,"span":14,"blocks":15},"col-1794121050506-fca52a",12,[16,21],{"id":17,"text":18,"type":19,"style":20},"block-1794121050506-5a99dd","1. Inline and displayed formulas","text","subheading",{"id":22,"text":23,"type":19,"style":24},"block-1794121050506-8c51aa","Enclose an inline formula in `\\$ ... \\$`. For example, `\\$\\sum_{i=0}^n i^2=\\frac{n(n+1)(2n+1)}{6}\\$` produces $\\sum_{i=0}^n i^2=\\frac{n(n+1)(2n+1)}{6}$.\n\nUse `\\$\\$ ... \\$\\$` to place a formula on a separate line. The `\\$ ... \\$` delimiters are explicitly enabled in QazMath; they are not enabled in MathJax by default.","paragraph",{"id":26,"columns":27},"row-1794121050506-aef665",[28],{"id":29,"span":14,"blocks":30},"col-1794121050506-921ecd",[31,34],{"id":32,"text":33,"type":19,"style":20},"block-1794121050506-35a728","2. Greek letters",{"id":35,"text":36,"type":19,"style":24},"block-1794121050506-7d7276","Lowercase letters: `\\alpha` — $\\alpha$, `\\beta` — $\\beta$, `\\gamma` — $\\gamma$, `\\epsilon` — $\\epsilon$, `\\varepsilon` — $\\varepsilon$, `\\phi` — $\\phi$, `\\varphi` — $\\varphi$, `\\omega` — $\\omega$.\n\nUppercase letters: `\\Gamma` — $\\Gamma$, `\\Delta` — $\\Delta$, `\\Theta` — $\\Theta$, `\\Lambda` — $\\Lambda$, `\\Pi` — $\\Pi$, `\\Omega` — $\\Omega$.",{"id":38,"columns":39},"row-1794121050506-f760d4",[40],{"id":41,"span":14,"blocks":42},"col-1794121050506-0eec28",[43,46],{"id":44,"text":45,"type":19,"style":20},"block-1794121050506-e2ef29","3. Superscripts and subscripts",{"id":47,"text":48,"type":19,"style":24},"block-1794121050506-a39006","Use `^` for a superscript and `_` for a subscript. Examples: `x_i^2` — $x_i^2$, `\\log_2 x` — $\\log_2 x$, `a_{n+1}` — $a_{n+1}$.",{"id":50,"columns":51},"row-1794121050506-43e702",[52],{"id":53,"span":14,"blocks":54},"col-1794121050506-b56fc2",[55,58],{"id":56,"text":57,"type":19,"style":20},"block-1794121050506-51bbd5","4. Grouping expressions",{"id":59,"text":60,"type":19,"style":24},"block-1794121050506-612968","Place several characters inside braces when they should form one superscript or subscript. In `10^10`, the superscript applies only to the first `1`; the correct form is `10^{10}`: $10^{10}$.\n\nWrite nested powers as `{x^y}^z` — ${x^y}^z$ or `x^{y^z}` — $x^{y^z}$. Other examples: `x_{i^2}` — $x_{i^2}$, `{x_i}^2` — ${x_i}^2$.",{"id":62,"columns":63},"row-1794121050506-5b11c3",[64],{"id":65,"span":14,"blocks":66},"col-1794121050506-5a40f4",[67,70],{"id":68,"text":69,"type":19,"style":20},"block-1794121050506-d5c6c2","5. Delimiters and brackets",{"id":71,"text":72,"type":19,"style":24},"block-1794121050506-c5fc11","Ordinary brackets can be typed directly: `(2+3)[4+4]` — $(2+3)[4+4]$. Their size, however, does not change to match the enclosed expression.\n\nUse `\\left` and `\\right` when brackets need to fit a large expression: $\\left(\\frac{\\frac{x+5}{x-3}}{x^2+5}\\right)$.\n\nThe same approach works for an absolute value, `\\left|x\\right|` — $\\left|x\\right|$, and braces, `\\left\\{x+1\\right\\}` — $\\left\\{x+1\\right\\}$.",{"id":74,"columns":75},"row-1794121050506-3a51a7",[76],{"id":77,"span":14,"blocks":78},"col-1794121050506-6415eb",[79,82],{"id":80,"text":81,"type":19,"style":20},"block-1794121050506-0593eb","6. Fractions",{"id":83,"text":84,"type":19,"style":24},"block-1794121050506-d22183","Write a fraction as `\\frac{a+1}{b+1}`: $\\frac{a+1}{b+1}$. If nested fractions look too small in inline text, use `\\dfrac`: $\\dfrac{\\dfrac{\\dfrac{x+5}{x^3}}{x-3}}{x^2+5}$.",{"id":86,"columns":87},"row-1794121050506-62b659",[88],{"id":89,"span":14,"blocks":90},"col-1794121050506-b85fa4",[91,94],{"id":92,"text":93,"type":19,"style":20},"block-1794121050506-16e4d7","7. Roots",{"id":95,"text":96,"type":19,"style":24},"block-1794121050506-6ea676","Write a square root as `\\sqrt{x^3}`: $\\sqrt{x^3}$. For a cube root or an $n$th root, put the degree in square brackets: `\\sqrt[3]{\\frac{x}{y}}` — $\\sqrt[3]{\\frac{x}{y}}$, `\\sqrt[n]{a}` — $\\sqrt[n]{a}$.",{"id":98,"columns":99},"row-1794121050506-35f4c9",[100],{"id":101,"span":14,"blocks":102},"col-1794121050506-69d51e",[103,106],{"id":104,"text":105,"type":19,"style":20},"block-1794121050506-7ff59e","8. Functions and limits",{"id":107,"text":108,"type":19,"style":24},"block-1794121050506-08b2c0","Put a backslash before a standard function name so that it appears upright and has the correct spacing before its argument: `\\sin x` — $\\sin x$, while `sin x` — $sin x$.\n\nCommon commands include `\\cos`, `\\tan`, `\\cot`, `\\log`, `\\ln`, `\\max`, `\\min`, and `\\sum`. Limit example: `\\lim_{x\\to 0}\\frac{\\sin x}{x}=1` — $\\lim_{x\\to 0}\\frac{\\sin x}{x}=1$.",{"id":110,"columns":111},"row-1794121050506-1d1aeb",[112],{"id":113,"span":14,"blocks":114},"col-1794121050506-aaf551",[115,118],{"id":116,"text":117,"type":19,"style":20},"block-1794121050506-2dfc57","9. Common symbols",{"id":119,"text":120,"type":19,"style":24},"block-1794121050506-22d587","`\\lt \\gt \\le \\ge \\neq` — $\\lt\\; \\gt\\; \\le\\; \\ge\\; \\neq$\n`\\times \\div \\pm \\mp \\cdot` — $\\times\\; \\div\\; \\pm\\; \\mp\\; \\cdot$\n`\\cup \\cap \\setminus \\subset \\subseteq \\supset \\in \\notin \\varnothing` — $\\cup\\; \\cap\\; \\setminus\\; \\subset\\; \\subseteq\\; \\supset\\; \\in\\; \\notin\\; \\varnothing$\n`\\binom{n+1}{2k}` — $\\binom{n+1}{2k}$\n`\\to \\gets \\Rightarrow \\Leftarrow \\mapsto \\implies \\iff` — $\\to\\; \\gets\\; \\Rightarrow\\; \\Leftarrow\\; \\mapsto\\; \\implies\\; \\iff$\n`\\land \\lor \\lnot \\forall \\exists \\top \\bot \\vdash \\vDash` — $\\land\\; \\lor\\; \\lnot\\; \\forall\\; \\exists\\; \\top\\; \\bot\\; \\vdash\\; \\vDash$\n`\\star \\ast \\oplus \\circ \\bullet \\infty` — $\\star\\; \\ast\\; \\oplus\\; \\circ\\; \\bullet\\; \\infty$\n`90^\\circ` — $90^\\circ$\n`\\approx \\sim \\simeq \\cong \\equiv` — $\\approx\\; \\sim\\; \\simeq\\; \\cong\\; \\equiv$\n`\\dots \\cdots` — $a_1,a_2,\\dots,a_n$ and $a_1+a_2+\\cdots+a_{80}$",{"id":122,"columns":123},"row-1794121050506-a39c75",[124],{"id":125,"span":14,"blocks":126},"col-1794121050506-d06fb2",[127,130],{"id":128,"text":129,"type":19,"style":20},"block-1794121050506-2ccabc","10. Spacing in formulas",{"id":131,"text":132,"type":19,"style":24},"block-1794121050506-dd6166","Most ordinary spaces inside a formula are ignored. Use `\\,`, `\\;`, `\\quad`, and `\\qquad` to add specific amounts of space: `a\\,b \\quad a\\;b \\qquad a b` — $a\\,b \\quad a\\;b \\qquad a b$.",{"id":134,"columns":135},"row-1794121050506-1e6608",[136],{"id":137,"span":14,"blocks":138},"col-1794121050506-5407c2",[139,142],{"id":140,"text":141,"type":19,"style":20},"block-1794121050506-96eb38","11. Systems of equations and matrices",{"id":143,"text":144,"type":19,"style":24},"block-1794121050506-5c81f4","Use `\\\\` to separate rows and `&` to separate or align columns.\n\nSystem of equations: `\\begin{cases} x+y=5 \\\\ x-y=1 \\end{cases}` — $\\begin{cases}x+y=5\\\\x-y=1\\end{cases}$.\n\nMatrix: `\\begin{pmatrix} 1 & 2 \\\\ 3 & 4 \\end{pmatrix}` — $\\begin{pmatrix}1&2\\\\3&4\\end{pmatrix}$.",{"id":146,"columns":147},"row-1794121050506-590427",[148],{"id":149,"span":14,"blocks":150},"col-1794121050506-b82d97",[151,154],{"id":152,"text":153,"type":19,"style":20},"block-1794121050506-01f9b6","12. Text and notation inside formulas",{"id":155,"text":156,"type":19,"style":24},"block-1794121050506-b24df1","Use `\\text{...}` to place ordinary text inside a formula: `x>0\\text{ when}` — $x>0\\text{ when}$.\n\nSegments, vectors, and other notation: `\\overline{AB}` — $\\overline{AB}$, `\\vec{a}` — $\\vec{a}$, `\\hat{x}` — $\\hat{x}$, `x\\in\\mathbb{R}` — $x\\in\\mathbb{R}$.",{"id":158,"columns":159},"row-1794121050506-c9108f",[160],{"id":161,"span":14,"blocks":162},"col-1794121050506-b27eb3",[163,166],{"id":164,"text":165,"type":19,"style":20},"block-1794121050506-5ebc3e","13. Common mistakes",{"id":167,"text":168,"type":19,"style":24},"block-1794121050506-2470f8","• Always close an opening formula delimiter: `\\$...\\$` or `\\$\\$...\\$\\$`.\n• Put a multi-character superscript, subscript, or argument inside `{...}`.\n• Do not omit the `\\` before a command name: `\\sin`, `\\sqrt`, `\\frac`.\n• Write an ordinary dollar sign in text as `\\$` so that it is not treated as the start of a formula.",{"id":170,"columns":171},"row-1794121050506-11e6c4",[172],{"id":173,"span":14,"blocks":174},"col-1794121050506-119126",[175,178],{"id":176,"text":177,"type":19,"style":20},"block-1794121050506-23cf56","Further reference",{"id":179,"text":180,"type":19,"style":24},"block-1794121050506-3517a4","Complete command list: https:\u002F\u002Fdocs.mathjax.org\u002Fen\u002Fstable\u002Finput\u002Ftex\u002Fmacros\u002F\n\nShort practical examples: https:\u002F\u002Fmath.meta.stackexchange.com\u002Fquestions\u002F5020\u002Fmathjax-basic-tutorial-and-quick-reference",{},"SSG",true,{},null,"2026-11-08T06:59:17.296Z","QazMath редакциясы","en",[190,191,188],"kz","ru",1794131266339]