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  "body": "\n## Definition\n\nA subset $I$ of $\\mathbb{R}$ is an interval when, for all $x$ and $y$ in $I$ and each real $z$ with $x \\le z \\le y$, also $z \\in I$.\nFor real numbers $a \\le b$, the notation is:\n$$[a, b] = \\{x \\in \\mathbb{R} : a \\le x \\le b\\}, \\qquad (a, b) = \\{x \\in \\mathbb{R} : a \u003c x \u003c b\\},$$\n$$[a, b) = \\{x \\in \\mathbb{R} : a \\le x \u003c b\\}, \\qquad (a, b] = \\{x \\in \\mathbb{R} : a \u003c x \\le b\\}.$$\nThe set $[a, b]$ is a closed interval and $(a, b)$ is an open interval.\nFor each real $a$, the notation is $[a, \\infty) = \\{x : x \\ge a\\}$, $(a, \\infty) = \\{x : x \u003e a\\}$, $(-\\infty, a] = \\{x : x \\le a\\}$ and $(-\\infty, a) = \\{x : x \u003c a\\}$.\n\n## Remarks\n\nBy the [[completeness axiom|0AXWET80YW]], each interval is one of the sets above, or $\\mathbb{R}$, or $\\emptyset$.\nIn some countries, the notation $]a, b[$ replaces $(a, b)$.\nThe symbols $\\infty$ and $-\\infty$ are not real numbers. They show only that the interval has no bound on that side.\n\n## Explanations\n\n### L1 human\n\nAn interval is a piece of the number line without holes.\nA square bracket means that the end point belongs to the interval, and a round bracket means that it does not.\nFor example, $[0, 1)$ contains $0$ and $0.999$, but not $1$.\n",
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