> ## Documentation Index
> Fetch the complete documentation index at: https://resources.latex-cloud-studio.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Math Mode

> Mathematical typesetting commands and environments in LaTeX

export const RenderedOutput = ({title = "Rendered output", ctaHref, ctaLabel = "Open LaTeX Cloud Studio", children}) => {
  const [isExpanded, setIsExpanded] = useState(false);
  const trackEditorCta = () => {
    const target = new URL(ctaHref, window.location.href);
    globalThis.posthog?.capture?.("docs_app_cta_clicked", {
      source_page: window.location.pathname,
      source_section: "rendered_output",
      cta_variant: "first_compiled_example",
      target_url: target.toString(),
      target_utm_source: target.searchParams.get("utm_source"),
      target_utm_medium: target.searchParams.get("utm_medium"),
      target_utm_campaign: target.searchParams.get("utm_campaign"),
      target_utm_content: target.searchParams.get("utm_content")
    }, {
      transport: "sendBeacon",
      send_instantly: true
    });
  };
  return <details className="rendered-output" onToggle={event => setIsExpanded(event.currentTarget.open)}>
      <summary className="rendered-output__summary">
        <span className="rendered-output__title">{title}</span>
        <span className="rendered-output__hint" aria-hidden="true">View compiled result</span>
      </summary>
      {isExpanded && <div className="rendered-output__content">
          {children}
          {ctaHref && <aside className="rendered-output__cta" aria-label="Continue in the LaTeX editor">
              <span>
                <strong>Ready to use this syntax?</strong>
                Continue in the browser editor when you want to adapt the example in a real project.
              </span>
              <a href={ctaHref} onClick={trackEditorCta}>{ctaLabel}<span aria-hidden="true"> →</span></a>
            </aside>}
        </div>}
    </details>;
};

export const LatexSource = ({filename, source}) => {
  const [copyStatus, setCopyStatus] = useState("Copy");
  const copySource = async () => {
    try {
      await navigator.clipboard.writeText(source);
      setCopyStatus("Copied");
    } catch {
      setCopyStatus("Select and copy");
    }
  };
  return <figure className="latex-source">
      <figcaption className="latex-source__header">
        <span className="latex-source__filename">{filename}</span>
        <button type="button" className="latex-source__copy" onClick={copySource} aria-live="polite">
          {copyStatus}
        </button>
      </figcaption>
      <pre className="latex-source__pre" aria-label={`LaTeX source: ${filename}`} tabIndex="0">
        <code className="language-latex">{source}</code>
      </pre>
    </figure>;
};

export const LatexPreview = ({src, alt, caption, width, height}) => {
  const minZoom = 1;
  const maxZoom = 3;
  const zoomStep = 0.5;
  const measureSvgContent = async (assetSrc, pageWidth, pageHeight) => {
    const cacheKey = "__latexCloudSvgContentBoxCache";
    const contentBoxCache = globalThis[cacheKey] ?? new Map();
    globalThis[cacheKey] = contentBoxCache;
    if (contentBoxCache.has(assetSrc)) return contentBoxCache.get(assetSrc);
    const measurement = (async () => {
      const assetUrl = new URL(assetSrc, window.location.href);
      if (assetUrl.origin !== window.location.origin) {
        throw new Error("Rendered output must use a same-origin SVG asset.");
      }
      const response = await fetch(assetUrl, {
        credentials: "same-origin"
      });
      if (!response.ok) throw new Error(`Rendered output request failed with ${response.status}.`);
      const source = await response.text();
      const documentNode = new DOMParser().parseFromString(source, "image/svg+xml");
      if (documentNode.querySelector("parsererror")) throw new Error("Rendered output is not valid SVG.");
      const sourceSvg = documentNode.documentElement;
      sourceSvg.querySelectorAll("script, foreignObject").forEach(node => node.remove());
      [sourceSvg, ...sourceSvg.querySelectorAll("*")].forEach(node => {
        [...node.attributes].forEach(attribute => {
          if ((/^on/i).test(attribute.name)) node.removeAttribute(attribute.name);
          if ((attribute.name === "href" || attribute.name === "xlink:href") && !attribute.value.startsWith("#")) {
            node.removeAttribute(attribute.name);
          }
        });
      });
      const measurementHost = document.createElement("div");
      measurementHost.className = "latex-preview__measurement-host";
      const measuredSvg = document.importNode(sourceSvg, true);
      measuredSvg.setAttribute("aria-hidden", "true");
      measurementHost.appendChild(measuredSvg);
      document.body.appendChild(measurementHost);
      try {
        const measuredElements = [...measuredSvg.children].filter(node => !["defs", "desc", "metadata", "style", "title"].includes(node.tagName.toLowerCase()));
        const elementBounds = measuredElements.map(node => node.getBBox()).filter(box => [box.x, box.y, box.width, box.height].every(Number.isFinite) && box.width > 0 && box.height > 0);
        if (elementBounds.length === 0) {
          throw new Error("Rendered output has no measurable visible content.");
        }
        const sortedBounds = [...elementBounds].sort((left, right) => left.y - right.y);
        const clusterGap = pageHeight * 0.045;
        const clusters = [];
        sortedBounds.forEach(box => {
          const current = clusters[clusters.length - 1];
          if (!current || box.y - current.bottom > clusterGap) {
            clusters.push({
              boxes: [box],
              bottom: box.y + box.height
            });
            return;
          }
          current.boxes.push(box);
          current.bottom = Math.max(current.bottom, box.y + box.height);
        });
        const contentClusters = clusters.filter(cluster => {
          const clusterBox = cluster.boxes.reduce((combined, box) => {
            const right = Math.max(combined.x + combined.width, box.x + box.width);
            const bottom = Math.max(combined.y + combined.height, box.y + box.height);
            const x = Math.min(combined.x, box.x);
            const y = Math.min(combined.y, box.y);
            return {
              x,
              y,
              width: right - x,
              height: bottom - y
            };
          });
          const centerY = clusterBox.y + clusterBox.height / 2;
          const isMarginFurniture = cluster.boxes.length <= 2 && clusterBox.width < pageWidth * 0.2 && clusterBox.height < pageHeight * 0.04 && (centerY < pageHeight * 0.08 || centerY > pageHeight * 0.8);
          return !isMarginFurniture;
        });
        const visibleBounds = (contentClusters.length > 0 ? contentClusters : clusters).flatMap(cluster => cluster.boxes);
        const bounds = visibleBounds.reduce((combined, box) => {
          const right = Math.max(combined.x + combined.width, box.x + box.width);
          const bottom = Math.max(combined.y + combined.height, box.y + box.height);
          const x = Math.min(combined.x, box.x);
          const y = Math.min(combined.y, box.y);
          return {
            x,
            y,
            width: right - x,
            height: bottom - y
          };
        });
        const clampValue = (value, minimum, maximum) => Math.min(maximum, Math.max(minimum, value));
        const padding = Math.max(8, Math.min(pageWidth, pageHeight) * 0.025);
        const x = clampValue(bounds.x - padding, 0, pageWidth);
        const y = clampValue(bounds.y - padding, 0, pageHeight);
        const right = clampValue(bounds.x + bounds.width + padding, 0, pageWidth);
        const bottom = clampValue(bounds.y + bounds.height + padding, 0, pageHeight);
        return {
          x,
          y,
          width: right - x,
          height: bottom - y
        };
      } finally {
        measurementHost.remove();
      }
    })();
    contentBoxCache.set(assetSrc, measurement);
    measurement.catch(() => contentBoxCache.delete(assetSrc));
    return measurement;
  };
  const renderPreviewAsset = ({contentBox: assetContentBox, loading}) => {
    if (!assetContentBox) {
      return <img className="latex-preview__asset" src={src} alt={alt} width={width} height={height} loading={loading} draggable="false" />;
    }
    return <svg className="latex-preview__asset" viewBox={`${assetContentBox.x} ${assetContentBox.y} ${assetContentBox.width} ${assetContentBox.height}`} preserveAspectRatio="xMidYMid meet" role="img" aria-label={alt}>
        <image href={src} x="0" y="0" width={width} height={height} />
      </svg>;
  };
  const [isOpen, setIsOpen] = useState(false);
  const [frameMode, setFrameMode] = useState("content");
  const [viewMode, setViewMode] = useState("fit");
  const [zoom, setZoom] = useState(minZoom);
  const [contentBox, setContentBox] = useState(null);
  const [measurementStatus, setMeasurementStatus] = useState("loading");
  const dialogRef = useRef(null);
  const closeButtonRef = useRef(null);
  const viewportRef = useRef(null);
  const previousFocusRef = useRef(null);
  const dragRef = useRef(null);
  useEffect(() => {
    let isCurrent = true;
    setMeasurementStatus("loading");
    measureSvgContent(src, width, height).then(box => {
      if (!isCurrent) return;
      setContentBox(box);
      setMeasurementStatus("ready");
    }).catch(() => {
      if (!isCurrent) return;
      setContentBox(null);
      setFrameMode("page");
      setMeasurementStatus("error");
    });
    return () => {
      isCurrent = false;
    };
  }, [height, src, width]);
  const closeViewer = useCallback(() => {
    setIsOpen(false);
  }, []);
  const openViewer = () => {
    previousFocusRef.current = document.activeElement;
    setFrameMode(contentBox ? "content" : "page");
    setViewMode("fit");
    setZoom(minZoom);
    setIsOpen(true);
  };
  const applyZoom = useCallback(nextZoom => {
    const boundedZoom = Math.min(maxZoom, Math.max(minZoom, nextZoom));
    setViewMode("custom");
    setZoom(boundedZoom);
  }, []);
  const zoomIn = useCallback(() => {
    applyZoom(viewMode === "fit" ? minZoom + zoomStep : zoom + zoomStep);
  }, [applyZoom, viewMode, zoom]);
  const zoomOut = useCallback(() => {
    applyZoom(viewMode === "fit" ? minZoom : zoom - zoomStep);
  }, [applyZoom, viewMode, zoom]);
  useEffect(() => {
    if (!isOpen) return undefined;
    const previousOverflow = document.body.style.overflow;
    document.body.style.overflow = "hidden";
    closeButtonRef.current?.focus();
    return () => {
      document.body.style.overflow = previousOverflow;
      previousFocusRef.current?.focus?.();
    };
  }, [isOpen]);
  useEffect(() => {
    if (!isOpen) return undefined;
    const handleKeyDown = event => {
      if (event.key === "Escape") {
        event.preventDefault();
        closeViewer();
        return;
      }
      if ((event.key === "+" || event.key === "=") && !event.metaKey && !event.ctrlKey) {
        event.preventDefault();
        zoomIn();
        return;
      }
      if (event.key === "-" && !event.metaKey && !event.ctrlKey) {
        event.preventDefault();
        zoomOut();
        return;
      }
      if (event.key !== "Tab" || !dialogRef.current) return;
      const focusable = [...dialogRef.current.querySelectorAll('button:not([disabled]), a[href], [tabindex]:not([tabindex="-1"])')];
      if (focusable.length === 0) return;
      const first = focusable[0];
      const last = focusable[focusable.length - 1];
      if (event.shiftKey && document.activeElement === first) {
        event.preventDefault();
        last.focus();
      } else if (!event.shiftKey && document.activeElement === last) {
        event.preventDefault();
        first.focus();
      }
    };
    window.addEventListener("keydown", handleKeyDown);
    return () => {
      window.removeEventListener("keydown", handleKeyDown);
    };
  }, [closeViewer, isOpen, zoomIn, zoomOut]);
  const startDrag = event => {
    if (event.button !== 0 || !viewportRef.current) return;
    const viewport = viewportRef.current;
    dragRef.current = {
      pointerId: event.pointerId,
      x: event.clientX,
      y: event.clientY,
      scrollLeft: viewport.scrollLeft,
      scrollTop: viewport.scrollTop
    };
    viewport.setPointerCapture(event.pointerId);
    viewport.dataset.dragging = "true";
  };
  const continueDrag = event => {
    const drag = dragRef.current;
    const viewport = viewportRef.current;
    if (!drag || !viewport || drag.pointerId !== event.pointerId) return;
    viewport.scrollLeft = drag.scrollLeft - (event.clientX - drag.x);
    viewport.scrollTop = drag.scrollTop - (event.clientY - drag.y);
  };
  const stopDrag = event => {
    const viewport = viewportRef.current;
    if (viewport?.hasPointerCapture(event.pointerId)) viewport.releasePointerCapture(event.pointerId);
    if (viewport) delete viewport.dataset.dragging;
    dragRef.current = null;
  };
  const activeContentBox = frameMode === "content" ? contentBox : null;
  const activeWidth = activeContentBox?.width ?? width;
  const activeHeight = activeContentBox?.height ?? height;
  const activeRatio = activeWidth / activeHeight;
  const inlineContentBox = measurementStatus === "ready" ? contentBox : null;
  const inlineWidth = inlineContentBox?.width ?? width;
  const inlineHeight = inlineContentBox?.height ?? height;
  const inlineGeometry = {
    aspectRatio: `${inlineWidth} / ${inlineHeight}`,
    maxWidth: `${30 * inlineWidth / inlineHeight}rem`
  };
  const imageStyle = viewMode === "fit" ? {
    aspectRatio: `${activeWidth} / ${activeHeight}`,
    width: "100%",
    maxWidth: `${Math.max(16, activeRatio * 78)}dvh`
  } : {
    aspectRatio: `${activeWidth} / ${activeHeight}`,
    width: `${zoom * 100}%`,
    maxWidth: "none"
  };
  const zoomLabel = viewMode === "fit" ? frameMode === "content" ? "Fit content" : "Full page" : `${Math.round(zoom * 100)}%`;
  return <figure className="latex-preview">
      <button type="button" className="latex-preview__trigger" onClick={openViewer} aria-haspopup="dialog" aria-label={`Open zoomable preview: ${alt}`}>
        <span className="latex-preview__page" style={inlineGeometry}>
          {measurementStatus === "loading" ? <span className="latex-preview__loading" role="status">Preparing compiled output…</span> : renderPreviewAsset({
    src,
    alt,
    width,
    height,
    contentBox: inlineContentBox,
    loading: "lazy"
  })}
        </span>
        <span className="latex-preview__trigger-label" aria-hidden="true">
          <span className="latex-preview__trigger-icon">⌕</span>
          Open viewer
        </span>
      </button>
      <figcaption className="latex-preview__caption">
        <span>
          {caption}
          {measurementStatus === "error" && <span className="latex-preview__status" role="status"> Content fit is unavailable; the complete vector page is shown.</span>}
        </span>
        <a href={src} target="_blank" rel="noreferrer" className="latex-preview__source-link">Open SVG</a>
      </figcaption>

      {isOpen && <div className="latex-preview__backdrop" onMouseDown={event => {
    if (event.target === event.currentTarget) closeViewer();
  }}>
          <section ref={dialogRef} className="latex-preview__dialog" role="dialog" aria-modal="true" aria-label={`Rendered LaTeX viewer: ${alt}`}>
            <header className="latex-preview__toolbar">
              <div className="latex-preview__identity">
                <span className="latex-preview__eyebrow">Compiled LaTeX</span>
                <span className="latex-preview__filename">{alt}</span>
              </div>
              <div className="latex-preview__controls" aria-label="Preview controls">
                <button type="button" className={frameMode === "content" && viewMode === "fit" ? "is-active" : undefined} disabled={!contentBox} onClick={() => {
    setFrameMode("content");
    setViewMode("fit");
    setZoom(minZoom);
  }}>
                  Fit content
                </button>
                <button type="button" className={frameMode === "page" && viewMode === "fit" ? "is-active" : undefined} onClick={() => {
    setFrameMode("page");
    setViewMode("fit");
    setZoom(minZoom);
  }}>
                  Full page
                </button>
                <span className="latex-preview__zoom-group">
                  <button type="button" onClick={zoomOut} disabled={viewMode === "fit" || zoom <= minZoom} aria-label="Zoom out">−</button>
                  <output aria-live="polite" aria-label="Current zoom">{zoomLabel}</output>
                  <button type="button" onClick={zoomIn} disabled={viewMode !== "fit" && zoom >= maxZoom} aria-label="Zoom in">+</button>
                </span>
                <a href={src} target="_blank" rel="noreferrer">Open SVG</a>
                <button ref={closeButtonRef} type="button" className="latex-preview__close" onClick={closeViewer} aria-label="Close rendered LaTeX viewer">
                  Close
                </button>
              </div>
            </header>
            <div ref={viewportRef} className="latex-preview__viewport" data-view-mode={viewMode} onPointerDown={startDrag} onPointerMove={continueDrag} onPointerUp={stopDrag} onPointerCancel={stopDrag}>
              <span className="latex-preview__dialog-page" style={imageStyle}>
                {renderPreviewAsset({
    src,
    alt,
    width,
    height,
    contentBox: activeContentBox
  })}
              </span>
            </div>
            <footer className="latex-preview__viewer-note">
              Compiler-generated vector output · Use +/− to zoom · Drag to pan · Esc to close
            </footer>
          </section>
        </div>}
    </figure>;
};

LaTeX excels at typesetting mathematical content. This reference covers math mode basics, symbols, equations, and advanced mathematical structures.

## Math Mode Basics

LaTeX has two math modes:

<CardGroup cols={2}>
  <Card title="Inline Math" icon="equals">
    Math within text: $a^2 + b^2 = c^2$
  </Card>

  <Card title="Display Math" icon="square-root-variable">
    Math on separate lines with automatic centering
  </Card>
</CardGroup>

### Entering Math Mode

<LatexSource filename="example.tex" source={"% Dollar signs (most common)\nThe equation $E = mc^2$ is famous.\n\n% \\(...\\) delimiters\nThe equation \\(E = mc^2\\) is famous.\n\n% math environment\nThe equation \\begin{math}E = mc^2\\end{math} is famous."} />

<RenderedOutput title="Rendered output" ctaHref="https://app.latex-cloud-studio.com/?utm_source=resources&utm_medium=rendered_output&utm_campaign=docs_open_app&utm_content=components_math_mode">
  <LatexPreview src="/images/rendered/components-math-mode-01/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

<LatexSource filename="example.tex" source={"% Double dollars\n$$E = mc^2$$\n\n% \\[...\\] delimiters (recommended)\n\\[E = mc^2\\]\n\n% displaymath environment\n\\begin{displaymath}\nE = mc^2\n\\end{displaymath}\n\n% equation environment (numbered)\n\\begin{equation}\nE = mc^2\n\\end{equation}"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-02/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

<Warning>
  **Important:** Text-mode commands don't work in math mode. Use math-specific commands for formatting.
</Warning>

## Basic Math Commands

### Superscripts and Subscripts

<LatexSource filename="example.tex" source={"x^2              % Superscript\nx_i              % Subscript\nx^{10}           % Multi-character superscript\nx_{ij}           % Multi-character subscript\nx^2_i            % Both\nx^{y^z}          % Nested superscripts\n\\sum_{i=1}^{n}   % Limits on operators"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-03/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

### Fractions

<LatexSource filename="example.tex" source={"\\frac{a}{b}           % Standard fraction\n\\dfrac{a}{b}          % Display style fraction (larger)\n\\tfrac{a}{b}          % Text style fraction (smaller)\n\\sfrac{1}{2}          % Slanted fraction (nicefrac package)\n\\frac{1}{2+\\frac{1}{3}} % Nested fractions"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Roots

<LatexSource filename="example.tex" source={"\\sqrt{x}              % Square root\n\\sqrt[3]{x}           % Cube root\n\\sqrt[n]{x}           % nth root\n\\sqrt{\\frac{a}{b}}    % Root of fraction"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-05/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

## Greek Letters

### Lowercase Greek

<LatexSource filename="example.tex" source={"\\alpha    \\beta     \\gamma    \\delta\n\\epsilon  \\zeta     \\eta      \\theta\n\\iota     \\kappa    \\lambda   \\mu\n\\nu       \\xi       \\pi       \\rho\n\\sigma    \\tau      \\upsilon  \\phi\n\\chi      \\psi      \\omega\n\n% Variants\n\\varepsilon  \\vartheta  \\varpi\n\\varrho      \\varsigma  \\varphi"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Uppercase Greek

<LatexSource filename="example.tex" source={"\\Gamma    \\Delta    \\Theta    \\Lambda\n\\Xi       \\Pi       \\Sigma    \\Upsilon\n\\Phi      \\Psi      \\Omega"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

## Mathematical Operators

### Binary Operators

<LatexSource filename="example.tex" source={"+         -         \\times    \\div\n\\pm       \\mp       \\cdot     \\ast\n\\star     \\circ     \\bullet   \\oplus\n\\ominus   \\otimes   \\oslash   \\odot"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Relational Operators

<LatexSource filename="example.tex" source={"=         \\neq      <         >\n\\leq      \\geq      \\ll       \\gg\n\\approx   \\sim      \\simeq    \\cong\n\\equiv    \\propto   \\subset   \\supset\n\\in       \\ni       \\perp     \\parallel"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-09/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

### Arrows

<LatexSource filename="example.tex" source={"\\leftarrow     \\rightarrow    \\leftrightarrow\n\\Leftarrow     \\Rightarrow    \\Leftrightarrow\n\\uparrow       \\downarrow     \\updownarrow\n\\nearrow       \\searrow       \\swarrow\n\\nwarrow       \\mapsto        \\longmapsto"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Large Operators

<LatexSource filename="example.tex" source={"\\sum_{i=1}^{n}      % Summation\n\\prod_{i=1}^{n}     % Product\n\\int_{a}^{b}        % Integral\n\\oint               % Contour integral\n\\bigcup_{i=1}^{n}   % Union\n\\bigcap_{i=1}^{n}   % Intersection\n\\lim_{x \\to \\infty} % Limit"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-11/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

## Delimiters

### Basic Delimiters

<LatexSource filename="example.tex" source={"(x)        [x]        \\{x\\}      |x|\n\\langle x \\rangle    \\lceil x \\rceil\n\\lfloor x \\rfloor    \\| x \\|"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Automatic Sizing

<LatexSource filename="example.tex" source={"% Manual sizing\n\\big( \\Big( \\bigg( \\Bigg(\n\n% Automatic sizing (recommended)\n\\left( \\frac{a}{b} \\right)\n\\left[ \\sum_{i=1}^{n} x_i \\right]\n\\left\\{ x : x > 0 \\right\\}\n\\left. \\frac{df}{dx} \\right|_{x=0}"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

## Mathematical Environments

### Single Equations

<LatexSource filename="example.tex" source={"% Numbered equation\n\\begin{equation}\nE = mc^2\n\\label{eq:einstein}\n\\end{equation}\n\n% Unnumbered equation\n\\begin{equation*}\nE = mc^2\n\\end{equation*}"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-14/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

### Multiple Equations

<LatexSource filename="example.tex" source={"\\begin{align}\nx + y &= 5 \\\\\n2x - y &= 1\n\\end{align}\n\n% With custom alignment\n\\begin{align}\nf(x) &= x^2 + 2x + 1 \\\\\n     &= (x + 1)^2\n\\end{align}"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-15/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

<LatexSource filename="example.tex" source={"\\begin{gather}\nx + y = 5 \\\\\n2x - y = 1\n\\end{gather}\n\n% Multiple columns\n\\begin{gather}\na = b     \\qquad c = d \\\\\ne = f     \\qquad g = h\n\\end{gather}"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-16/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

<LatexSource filename="example.tex" source={"f(x) = \\begin{cases}\nx^2 & \\text{if } x \\geq 0 \\\\\n-x^2 & \\text{if } x < 0\n\\end{cases}"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-17/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

### Matrices

<LatexSource filename="example.tex" source={"% Basic matrix\n\\begin{matrix}\na & b \\\\\nc & d\n\\end{matrix}\n\n% Matrix with delimiters\n\\begin{pmatrix}        % Parentheses\na & b \\\\\nc & d\n\\end{pmatrix}\n\n\\begin{bmatrix}        % Brackets\na & b \\\\\nc & d\n\\end{bmatrix}\n\n\\begin{vmatrix}        % Vertical lines (determinant)\na & b \\\\\nc & d\n\\end{vmatrix}\n\n\\begin{Vmatrix}        % Double vertical lines\na & b \\\\\nc & d\n\\end{Vmatrix}"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

## Advanced Features

### Text in Math Mode

<LatexSource filename="example.tex" source={"% Basic text\n\\text{if } x > 0\n\n% Text with math inside\n\\text{for all } x \\in \\mathbb{R}\n\n% Common text operators\n\\sin x   \\cos x   \\tan x   \\log x\n\\exp x   \\max x   \\min x   \\det A"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Math Fonts

<LatexSource filename="example.tex" source={"\\mathbb{R}     % Blackboard bold (reals)\n\\mathbb{N}     % Natural numbers\n\\mathbb{Z}     % Integers\n\\mathbb{C}     % Complex numbers\n\n\\mathcal{L}    % Calligraphic\n\\mathscr{F}    % Script (mathrsfs package)\n\\mathfrak{g}   % Fraktur (amssymb package)\n\\mathbf{v}     % Bold (vectors)\n\\boldsymbol{\\alpha} % Bold Greek"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Spacing in Math

<LatexSource filename="example.tex" source={"% Automatic spacing (usually best)\na + b\n\n% Manual spacing\na \\, b         % Thin space\na \\: b         % Medium space\na \\; b         % Thick space\na \\quad b      % Quad space\na \\qquad b     % Double quad\n\n% Negative space\na \\! b         % Negative thin space"} />

<RenderedOutput title="Rendered output">
  <LatexPreview src="/images/rendered/components-math-mode-21/page-1.svg" alt="Compiled PDF page 1 from example.tex" caption="Generated from the shown source with pdfLaTeX in the pinned LaTeXCloud TeX Live 2026 environment. The visible fragment is compiled inside the documented minimal article wrapper." width={595.276} height={841.89} />
</RenderedOutput>

### Theorems and Proofs

<LatexSource filename="example.tex" source={"\\usepackage{amsthm}\n\n% Define theorem environments\n\\newtheorem{theorem}{Theorem}\n\\newtheorem{lemma}{Lemma}\n\\newtheorem{proof}{Proof}\n\n% Use in document\n\\begin{theorem}\nFor all $x \\in \\mathbb{R}$, we have $x^2 \\geq 0$.\n\\end{theorem}\n\n\\begin{proof}\nThis follows from the definition of real numbers.\n\\end{proof}"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

## Common Constructions

### Derivatives

<LatexSource filename="example.tex" source={"% Basic derivative\n\\frac{df}{dx}\n\n% Partial derivative\n\\frac{\\partial f}{\\partial x}\n\n% Higher derivatives\n\\frac{d^2f}{dx^2}\n\n% At a point\n\\left.\\frac{df}{dx}\\right|_{x=0}"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Integrals

<LatexSource filename="example.tex" source={"% Definite integral\n\\int_0^1 x^2 \\, dx\n\n% Indefinite integral\n\\int f(x) \\, dx\n\n% Multiple integrals\n\\iint_D f(x,y) \\, dx \\, dy\n\\iiint_V f(x,y,z) \\, dV"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

### Sums and Products

<LatexSource filename="example.tex" source={"% Sum\n\\sum_{n=1}^{\\infty} \\frac{1}{n^2}\n\n% Product\n\\prod_{i=1}^{n} x_i\n\n% Inline versions\n$\\sum\\limits_{i=1}^{n}$ % Forces display style\n$\\sum\\nolimits_{i=1}^{n}$ % Forces inline style"} />

<RenderedOutput title="Expected effect">
  <Info>
    This code is a contextual or intentionally partial LaTeX excerpt, not a self-contained compilable document. Its visible result depends on the surrounding document, so the documentation shows the expected role without inventing a standalone preview.
  </Info>
</RenderedOutput>

## Best Practices

<Tip>
  **Math typesetting tips:**

  1. **Use proper math mode** - Never use text italic for math
  2. **Choose appropriate environments** - `align` for equations that should align
  3. **Label important equations** - Use `\label{eq:descriptive-name}`
  4. **Use `\text{}` for words** - Don't write words directly in math mode
  5. **Let LaTeX handle spacing** - Avoid manual spacing unless necessary
</Tip>

## Quick Reference

| Symbol | Command   | Symbol | Command   |
| ------ | --------- | ------ | --------- |
| ±      | `\pm`     | ≤      | `\leq`    |
| ×      | `\times`  | ≥      | `\geq`    |
| ÷      | `\div`    | ≠      | `\neq`    |
| ∞      | `\infty`  | ≈      | `\approx` |
| ∑      | `\sum`    | ∈      | `\in`     |
| ∫      | `\int`    | ⊂      | `\subset` |
| √      | `\sqrt{}` | ∪      | `\cup`    |
| α      | `\alpha`  | ∩      | `\cap`    |

***

Next: Explore [Lists](/learn/latex/basics/lists) or learn about [Tables](/learn/latex/tables/creating-tables) for data presentation.