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  "body": "\n## Definition\n\nLet $X$ be a set.\nA sequence in $X$ is a function $a \\colon \\mathbb{N} \\to X$, where $\\mathbb{N} = \\{0, 1, 2, \\dots\\}$.\nThe value $a(n)$ is the $n$-th term of the sequence, with the notation $a_n$.\nThe notation for the sequence is $(a_n)_{n \\in \\mathbb{N}}$, or $(a_n)$ when the index set is clear.\n\n## Remarks\n\nMany texts start the index at $1$, and they use a function on $\\{1, 2, 3, \\dots\\}$. The theory does not change.\nThe terms of a sequence can repeat. For example, $(1, 0, 1, 0, \\dots)$ is the sequence with $a_n = 1$ for even $n$ and $a_n = 0$ for odd $n$.\nA sequence of real numbers is a [[real sequence|0CTV783HYT]].\n\n## Explanations\n\n### L1 human\n\nA sequence is an infinite list $a_0, a_1, a_2, \\dots$ of elements of a set.\nThe order matters, and the same element can occur more than once.\nFor example, the squares $0, 1, 4, 9, 16, \\dots$ form the sequence $a_n = n^2$.\n",
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