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</head>
<body>

  
  <div class="section">
    <div class="header-row">
      <div class="title-badge">
        <span>Discrete (ℤ)</span>
        <span class="tag">Integers</span>
      </div>
      <div class="rule-text">Immediate successor exists</div>
    </div>

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      <text x="200" y="68" font-size="14" font-weight="600" fill="#1e2945" text-anchor="middle">1</text>

      
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      <circle cx="340" cy="45" r="5" fill="#1e2945" />
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      <circle cx="480" cy="45" r="5" fill="#1e2945" />
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    </svg>
  </div>

  <div class="divider"></div>

  
  <div class="section">
    <div class="header-row">
      <div class="title-badge">
        <span>Dense (ℚ)</span>
        <span class="tag highlight">Rationals</span>
      </div>
      <div class="rule-text" id="densityRule">No immediate successor</div>
    </div>

    <svg id="denseSvg" viewBox="0 0 540 130" aria-label="Dense rational number line">
      
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      <text x="60" y="90" font-size="13" font-weight="700" fill="#1e2945" text-anchor="middle">a = 0</text>

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      <g id="annotationsLayer"></g>
    </svg>
  </div>

  
  <div class="controls">
    <button id="stepBtn" class="btn">
      <span>Bisect</span>
      <span style="font-size: 11px;">(a+b)/2 →</span>
    </button>
    <button id="resetBtn" class="btn btn-secondary">Reset</button>
    <div class="step-indicators">
      <div class="step-dot active" data-step="0"></div>
      <div class="step-dot" data-step="1"></div>
      <div class="step-dot" data-step="2"></div>
      <div class="step-dot" data-step="3"></div>
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</body>
</html>

Structural Hierarchy of Number Systems

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
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      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 16px 12px;
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    .header-bar {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      width: 100%;
    }

    .set-tag {
      font-size: 15px;
      font-weight: 600;
      color: #334155;
      background: #f1f5f9;
      padding: 4px 14px;
      border-radius: 20px;
      letter-spacing: 0.2px;
    }

    .toggle-group {
      display: flex;
      background: #e2e8f0;
      border-radius: 8px;
      padding: 3px;
      gap: 2px;
    }

    .toggle-btn {
      border: none;
      background: transparent;
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    }

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      background: #ffffff;
      color: #0284c7;
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      background: #fef2f2;
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      border: 1px solid #fecaca;
    }

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      background: #ecfdf5;
      color: #059669;
      border: 1px solid #a7f3d0;
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  </style>
</head>
<body>

  <div class="header-bar">
    <div class="set-tag">S = { q ∈ ℚ : q &gt; 0, q² &lt; 2 }</div>
    <div class="toggle-group" role="tablist">
      <button class="toggle-btn active" id="btnQ" onclick="setMode('Q')">ℚ (Rationals)</button>
      <button class="toggle-btn" id="btnR" onclick="setMode('R')">ℝ (Reals)</button>
    </div>
  </div>

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    <svg viewBox="0 0 540 210" aria-label="Number line diagram">
      
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      <text x="210" y="98" fill="#0284c7" font-size="13" font-weight="700" text-anchor="middle">Set S (q² &lt; 2)</text>

      
      
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      <text x="90" y="146" fill="#64748b" font-size="13" font-weight="600" text-anchor="middle">0</text>

      
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      <text x="230" y="146" fill="#64748b" font-size="13" font-weight="600" text-anchor="middle">1</text>
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      <text x="330" y="146" fill="#64748b" font-size="12" font-weight="500" text-anchor="middle">1.4</text>
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      <line x1="365" y1="116" x2="365" y2="124" stroke="#94a3b8" stroke-width="1.5" />
      <text x="365" y="162" fill="#64748b" font-size="11" font-weight="500" text-anchor="middle">1.414…</text>
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      <text x="470" y="146" fill="#64748b" font-size="13" font-weight="600" text-anchor="middle">2</text>

      
      
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      <text x="382" y="184" fill="#dc2626" font-size="13" font-weight="700" text-anchor="middle" id="coordLabel">√2 ∉ ℚ</text>
    </svg>
  </div>

  <div id="statusMessage" class="status-card status-q">
    Supremum does not exist in ℚ
  </div>

  <script>
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      document.getElementById('btnR').classList.toggle('active', isR);

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        hole.setAttribute('r', '7');
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</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
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      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px;
      min-height: 100%;
      user-select: none;
    }

    /* Controls */
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      display: flex;
      gap: 6px;
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      max-width: 480px;
      justify-content: center;
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      flex: 1;
      padding: 6px 4px;
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      font-weight: 700;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      background: #f8fafc;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: all 0.2s ease;
    }
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      border-color: #94a3b8;
      box-shadow: 0 2px 4px rgba(0,0,0,0.06);
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    /* Nested Hierarchy Container */
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      position: relative;
      width: 100%;
      max-width: 480px;
      height: 240px;
      margin: 0 auto;
    }

    /* Concentric boxes */
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    /* Info Strip */
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      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      margin-top: 8px;
      min-height: 48px;
    }
    .equation-badge {
      font-size: 13px;
      font-weight: 700;
      font-family: monospace;
      padding: 4px 8px;
      border-radius: 6px;
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #0f172a;
      white-space: nowrap;
    }
    .property-tag {
      font-size: 12px;
      font-weight: 700;
      text-align: right;
      color: #334155;
    }
  </style>
</head>
<body>

  
  <div class="nav-bar">
    <button class="tier-btn" data-tier="N">ℕ Natural</button>
    <button class="tier-btn" data-tier="Z">ℤ Integers</button>
    <button class="tier-btn" data-tier="Q">ℚ Rationals</button>
    <button class="tier-btn active" data-tier="R">ℝ Reals</button>
  </div>

  
  <div class="diagram-stage">
    
    <div class="set-box highlight" id="box-R" data-tier="R">
      <div class="set-header">
        <span class="set-symbol" style="color:#6b21a8;">ℝ Reals</span>
        <span class="set-samples" style="color:#6b21a8;">π, √2, e</span>
      </div>

      
      <div class="set-box" id="box-Q" data-tier="Q">
        <div class="set-header">
          <span class="set-symbol" style="color:#0369a1;">ℚ Rationals</span>
          <span class="set-samples" style="color:#0369a1;">½, -¾, 0.25</span>
        </div>

        
        <div class="set-box" id="box-Z" data-tier="Z">
          <div class="set-header">
            <span class="set-symbol" style="color:#15803d;">ℤ Integers</span>
            <span class="set-samples" style="color:#15803d;">-3, -1, 0</span>
          </div>

          
          <div class="set-box" id="box-N" data-tier="N">
            <div class="set-header">
              <span class="set-symbol" style="color:#a16207;">ℕ Natural</span>
              <span class="set-samples" style="color:#a16207;">1, 2, 3...</span>
            </div>
          </div>

        </div>
      </div>
    </div>
  </div>

  
  <div class="info-card" id="infoCard">
    <div class="equation-badge" id="eqBadge">x² = 2 → x = √2</div>
    <div class="property-tag" id="propTag">Completeness (No Gaps)</div>
  </div>

  <script>
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        eq: 'Counting: 1, 2, 3...',
        prop: 'Closure under + and ×'
      },
      Z: {
        eq: 'x + 3 = 1 → x = -2',
        prop: '+ Additive Inverses'
      },
      Q: {
        eq: '2x = 3 → x = 3/2',
        prop: '× Multiplicative Inverses'
      },
      R: {
        eq: 'x² = 2 → x = √2',
        prop: 'Completeness (Continuous)'
      }
    };

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        selectTier(box.dataset.tier);
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  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
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      background: transparent;
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      display: flex;
      flex-direction: column;
      gap: 8px;
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    .selector-bar {
      display: flex;
      justify-content: center;
      gap: 6px;
      flex-wrap: wrap;
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    .tab-btn {
      border: 1px solid #d1d5db;
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      color: #1e2945;
      font-size: 13px;
      font-weight: 600;
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      cursor: pointer;
      transition: background-color 0.2s, border-color 0.2s, box-shadow 0.2s;
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    .tab-btn.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
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    .table-container {
      width: 100%;
      overflow-x: auto;
    }

    table {
      width: 100%;
      border-collapse: separate;
      border-spacing: 3px;
      table-layout: fixed;
    }

    th, td {
      text-align: center;
      vertical-align: middle;
      padding: 6px 2px;
      border-radius: 6px;
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    th {
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
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      text-align: left;
      font-size: 12px;
      font-weight: 600;
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    .set-header {
      background: #f1f5f9;
      font-size: 15px;
      font-weight: 700;
      padding: 6px 2px;
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    .badge-ok {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      background: #ecfdf5;
      color: #059669;
      border: 1px solid #a7f3d0;
      border-radius: 4px;
      font-size: 13px;
      font-weight: 700;
      padding: 3px 6px;
      min-width: 24px;
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    .badge-fail {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      background: #fef2f2;
      color: #dc2626;
      border: 1px solid #fecaca;
      border-radius: 4px;
      padding: 2px 3px;
      font-size: 10px;
      font-weight: 600;
      line-height: 1.1;
    }

    .badge-fail .icon {
      font-size: 12px;
      font-weight: 800;
      margin-bottom: 1px;
    }

    .type-badge {
      display: inline-block;
      font-size: 11px;
      font-weight: 700;
      padding: 4px 2px;
      border-radius: 4px;
      width: 100%;
      text-align: center;
      letter-spacing: -0.2px;
    }

    .type-semiring {
      background: #fffbeb;
      color: #b45309;
      border: 1px solid #fde68a;
    }

    .type-ring {
      background: #eff6ff;
      color: #1d4ed8;
      border: 1px solid #bfdbfe;
    }

    .type-field {
      background: #f5f3ff;
      color: #6d28d9;
      border: 1px solid #ddd6fe;
    }

    .dimmed {
      opacity: 0.3;
    }

    .highlight-col {
      box-shadow: 0 0 0 2px #1e2945 inset;
    }

    tr.row-bg td {
      background: #f8fafc;
    }

    .math-symbol {
      font-family: "Cambria Math", "Times New Roman", serif;
      font-weight: bold;
      font-size: 16px;
    }
  </style>
</head>
<body>

  <div class="selector-bar">
    <button class="tab-btn active" onclick="highlight('all')">All Sets</button>
    <button class="tab-btn" onclick="highlight('n')"><span class="math-symbol">ℕ</span></button>
    <button class="tab-btn" onclick="highlight('z')"><span class="math-symbol">ℤ</span></button>
    <button class="tab-btn" onclick="highlight('q')"><span class="math-symbol">ℚ</span></button>
    <button class="tab-btn" onclick="highlight('r')"><span class="math-symbol">ℝ</span></button>
  </div>

  <div class="table-container">
    <table>
      <thead>
        <tr>
          <th class="prop-col">Property</th>
          <th class="set-col col-n set-header"><span class="math-symbol">ℕ</span></th>
          <th class="set-col col-z set-header"><span class="math-symbol">ℤ</span></th>
          <th class="set-col col-q set-header"><span class="math-symbol">ℚ</span></th>
          <th class="set-col col-r set-header"><span class="math-symbol">ℝ</span></th>
        </tr>
      </thead>
      <tbody>
        <tr class="row-bg">
          <td class="prop-col">Addition (+)</td>
          <td class="set-col col-n"><span class="badge-ok">✓</span></td>
          <td class="set-col col-z"><span class="badge-ok">✓</span></td>
          <td class="set-col col-q"><span class="badge-ok">✓</span></td>
          <td class="set-col col-r"><span class="badge-ok">✓</span></td>
        </tr>
        <tr class="row-bg">
          <td class="prop-col">Subtraction (−)</td>
          <td class="set-col col-n">
            <div class="badge-fail">
              <span class="icon">✗</span>
              <span>2−5=−3</span>
            </div>
          </td>
          <td class="set-col col-z"><span class="badge-ok">✓</span></td>
          <td class="set-col col-q"><span class="badge-ok">✓</span></td>
          <td class="set-col col-r"><span class="badge-ok">✓</span></td>
        </tr>
        <tr class="row-bg">
          <td class="prop-col">Multiplication (×)</td>
          <td class="set-col col-n"><span class="badge-ok">✓</span></td>
          <td class="set-col col-z"><span class="badge-ok">✓</span></td>
          <td class="set-col col-q"><span class="badge-ok">✓</span></td>
          <td class="set-col col-r"><span class="badge-ok">✓</span></td>
        </tr>
        <tr class="row-bg">
          <td class="prop-col">Division (÷, ≠0)</td>
          <td class="set-col col-n">
            <div class="badge-fail">
              <span class="icon">✗</span>
              <span>1÷2=½</span>
            </div>
          </td>
          <td class="set-col col-z">
            <div class="badge-fail">
              <span class="icon">✗</span>
              <span>1÷2=½</span>
            </div>
          </td>
          <td class="set-col col-q"><span class="badge-ok">✓</span></td>
          <td class="set-col col-r"><span class="badge-ok">✓</span></td>
        </tr>
        <tr>
          <td class="prop-col">Structure</td>
          <td class="set-col col-n"><span class="type-badge type-semiring">Semiring</span></td>
          <td class="set-col col-z"><span class="type-badge type-ring">Ring</span></td>
          <td class="set-col col-q"><span class="type-badge type-field">Field</span></td>
          <td class="set-col col-r"><span class="type-badge type-field">Field</span></td>
        </tr>
      </tbody>
    </table>
  </div>

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      const buttons = document.querySelectorAll('.tab-btn');
      
      const sets = ['n', 'z', 'q', 'r'];
      
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        if (buttons[idx]) buttons[idx].classList.add('active');
        
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              el.classList.remove('dimmed');
              el.classList.add('highlight-col');
            } else {
              el.classList.add('dimmed');
              el.classList.remove('highlight-col');
            }
          });
        });
      }
    }
  </script>
</body>
</html>

OGM.13.NUM.1

Aligned learning resources

Related diagrams