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  "body": "\n## Description\n\nThe real numbers are the numbers that measure continuous quantities, such as lengths. We picture them as the points of a line.\nWe write $\\mathbb{R}$ for the set of real numbers.\nWith addition, multiplication and its order, $\\mathbb{R}$ is an [[ordered field|0QSPNASE50]].\nThis ordered field is complete: each nonempty subset of $\\mathbb{R}$ that is bounded above has a [[least upper bound|0AXWET80YW]].\nUp to a unique isomorphism, $\\mathbb{R}$ is the only [[complete ordered field|0A9E6X0S3E]].\n\n## Remarks\n\nThe set $\\mathbb{R}$ contains the [[rational numbers|0NCJ5WXN6Z]] and also [[irrational numbers|080T2TXVQV]] such as $\\sqrt{2}$ and $\\pi$.\nTwo common constructions of $\\mathbb{R}$ from $\\mathbb{Q}$ use [[Dedekind cuts|04QNZZ4HHY]] or [[Cauchy sequences|0D8HE681SC]].\nThe set $\\mathbb{R}$ is uncountable.\n\n## Explanations\n\n### L1 human\n\nThe real numbers fill the number line without gaps.\nThe rational numbers leave gaps, for example at $\\sqrt{2}$, and the real numbers fill these gaps.\nEach real number has a [[decimal expansion|06XY4X9430]], such as $3.14159\\dots$ for $\\pi$.\n",
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