{
  "id": "real-number",
  "domain": "number-theory",
  "type": "Concept",
  "title": "Real Number",
  "slug": "real-number",
  "url": "/mathematics/number-theory/real-number/",
  "summary": "Complete ordered field — all points on the continuous number line. Dedekind cuts (1872) and Cauchy sequences (Cantor 1872) as constructions. Least upper bound property. Uncountable (Cantor diagonal). Foundation of calculus and analysis.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Dedekind, R. (1872). Stetigkeit und irrationale Zahlen. Trans. Beman 1901."
    },
    {
      "tier": 1,
      "citation": "Rudin, W. (1976). Principles of Mathematical Analysis. 3rd ed."
    },
    {
      "tier": 2,
      "citation": "Spivak, M. (2008). Calculus. 4th ed. Publish or Perish."
    },
    {
      "tier": 3,
      "citation": "Stillwell, J. (2010). The Real Numbers. Springer."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}