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  "body": "\n## Summary\n\nA solution of a difference equation is oscillatory if it keeps changing sign, however far one goes along the sequence.\nA solution that is eventually of one sign is called nonoscillatory.\nOscillation theory looks for conditions on the coefficients that force all solutions, or some solutions, to oscillate.\nIt is the discrete counterpart of the [[oscillation theory|ZH2S50NSZ6]] of differential equations, such as Sturm theory.\n\n## Explanations\n\n### L1 human\n\nWatch the signs of the terms of a sequence.\nIf they settle down to always plus or always minus, the sequence does not oscillate.\nIf a sign change keeps happening again and again, it oscillates.\nThe solution $x_n = (-1)^n$ of $x_{n+1} = -x_n$ oscillates, while the solution $x_n = 2^n$ of $x_{n+1} = 2 x_n$ does not.\n",
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