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  "body": "\n## Summary\n\nA sequence of functions is a sequence $(f_n)$ of functions $f_n \\colon S \\to \\mathbb{R}$ on a common set $S$. For each fixed $x \\in S$, the values $f_n(x)$ form a [[sequence of real numbers|0QE8STGJH2]]. Such sequences can converge in several ways, mainly [[pointwise|056FSKG32J]] or [[uniformly|08FPABDQ4C]].\n\n## Remarks\n\nThe two modes give different properties of the limit. A uniform limit of continuous functions is continuous, but a pointwise limit need not be.\nExamples are the Taylor polynomials of a function, and the partial sums of a power series.\n\n## Explanations\n\n### L1 human\n\nA sequence of functions is a list of graphs, one for each $n$.\nWe ask whether the graphs approach the graph of a limit function, and in what sense.\n",
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