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We looked inside some of the posts by geminimatthias and here's what we found interesting.
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Text
"[-1 -1 0 0 0 0 0 0] [ 1 -1 0 0 0 0 0 0] [0, 1, 2, 3] 1\n",
"[-1 -1 0 0 0 0 0 0] [ 1 -1 0 0 0 0 0 0] [4, 5, 6, 7] 2\n",
"[-1 -1 0 0 0 0 0 0] [ 1 -1 0 0 0 0 0 0] [8, 9, 10, 11] 3\n",
"[-1 -1 0 0 0 0 0 0] [ 1 -1 0 0 0 0 0 0] [12, 13, 14, 15] 4\n",
"[-1 0 -1 0 0 0 0 0] [ 1 0 -1 0 0 0 0 0] [0, 1, 4, 5] 1\n",
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"[-1 0 -1 0 0 0 0 0] [ 1 0 -1 0 0 0 0 0] [8, 9, 12, 13] 3\n",
"[-1 0 -1 0 0 0 0 0] [ 1 0 -1 0 0 0 0 0] [10, 11, 14, 15] 4\n",
"[-1 -1 -1 0 0 0 0 0] [ 1 -1 -1 0 0 0 0 0] [0, 1, 6, 7] 1\n",
"[-1 -1 -1 0 0 0 0 0] [ 1 -1 -1 0 0 0 0 0] [8, 9, 14, 15] 2\n",
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"[-1 0 0 -1 0 0 0 0] [ 1 0 0 -1 0 0 0 0] [6, 7, 14, 15] 4\n",
"[-1 -1 0 -1 0 0 0 0] [ 1 -1 0 -1 0 0 0 0] [0, 1, 10, 11] 1\n",
"[-1 -1 0 -1 0 0 0 0] [ 1 -1 0 -1 0 0 0 0] [4, 5, 14, 15] 2\n",
"[-1 0 -1 -1 0 0 0 0] [ 1 0 -1 -1 0 0 0 0] [0, 1, 12, 13] 1\n",
"[-1 0 -1 -1 0 0 0 0] [ 1 0 -1 -1 0 0 0 0] [2, 3, 14, 15] 2\n",
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"[ 0 -1 -1 0 0 0 0 0] [ 0 1 -1 0 0 0 0 0] [1, 3, 5, 7] 2\n",
"[ 0 -1 -1 0 0 0 0 0] [ 0 1 -1 0 0 0 0 0] [8, 10, 12, 14] 3\n",
"[ 0 -1 -1 0 0 0 0 0] [ 0 1 -1 0 0 0 0 0] [9, 11, 13, 15] 4\n",
"[-1 -1 -1 0 0 0 0 0] [-1 1 -1 0 0 0 0 0] [0, 2, 5, 7] 1\n",
"[-1 -1 -1 0 0 0 0 0] [-1 1 -1 0 0 0 0 0] [8, 10, 13, 15] 2\n",
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"[ 0 -1 0 -1 0 0 0 0] [ 0 1 0 -1 0 0 0 0] [1, 3, 9, 11] 2\n",
"[ 0 -1 0 -1 0 0 0 0] [ 0 1 0 -1 0 0 0 0] [4, 6, 12, 14] 3\n",
"[ 0 -1 0 -1 0 0 0 0] [ 0 1 0 -1 0 0 0 0] [5, 7, 13, 15] 4\n",
"[-1 -1 0 -1 0 0 0 0] [-1 1 0 -1 0 0 0 0] [0, 2, 9, 11] 1\n",
"[-1 -1 0 -1 0 0 0 0] [-1 1 0 -1 0 0 0 0] [4, 6, 13, 15] 2\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 1 -1 -1 0 0 0 0] [0, 2, 12, 14] 1\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 1 -1 -1 0 0 0 0] [1, 3, 13, 15] 2\n",
"[-1 -1 -1 -1 0 0 0 0] [-1 1 -1 -1 0 0 0 0] [0, 2, 13, 15] 1\n",
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"[-1 -1 -1 0 0 0 0 0] [ 1 1 -1 0 0 0 0 0] [8, 11, 12, 15] 2\n",
"[-1 -1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [0, 3, 8, 11] 1\n",
"[-1 -1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [4, 7, 12, 15] 2\n",
"[-1 -1 -1 -1 0 0 0 0] [ 1 1 -1 -1 0 0 0 0] [0, 3, 12, 15] 1\n",
"[ 0 0 -1 -1 0 0 0 0] [ 0 0 1 -1 0 0 0 0] [0, 4, 8, 12] 1\n",
"[ 0 0 -1 -1 0 0 0 0] [ 0 0 1 -1 0 0 0 0] [1, 5, 9, 13] 2\n",
"[ 0 0 -1 -1 0 0 0 0] [ 0 0 1 -1 0 0 0 0] [2, 6, 10, 14] 3\n",
"[ 0 0 -1 -1 0 0 0 0] [ 0 0 1 -1 0 0 0 0] [3, 7, 11, 15] 4\n",
"[-1 0 -1 -1 0 0 0 0] [-1 0 1 -1 0 0 0 0] [0, 4, 9, 13] 1\n",
"[-1 0 -1 -1 0 0 0 0] [-1 0 1 -1 0 0 0 0] [2, 6, 11, 15] 2\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 -1 1 -1 0 0 0 0] [0, 4, 10, 14] 1\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 -1 1 -1 0 0 0 0] [1, 5, 11, 15] 2\n",
"[-1 -1 -1 -1 0 0 0 0] [-1 -1 1 -1 0 0 0 0] [0, 4, 11, 15] 1\n",
"[-1 0 -1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [0, 5, 8, 13] 1\n",
"[-1 0 -1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [2, 7, 10, 15] 2\n",
"[-1 -1 -1 -1 0 0 0 0] [ 1 -1 1 -1 0 0 0 0] [0, 5, 10, 15] 1\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [0, 6, 8, 14] 1\n",
"[ 0 -1 -1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [1, 7, 9, 15] 2\n",
"[-1 -1 -1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [0, 6, 9, 15] 1\n",
"[-1 -1 -1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [0, 7, 8, 15] 1\n",
"[ 1 -1 -1 0 0 0 0 0] [-1 1 -1 0 0 0 0 0] [1, 2, 5, 6] 1\n",
"[ 1 -1 -1 0 0 0 0 0] [-1 1 -1 0 0 0 0 0] [9, 10, 13, 14] 2\n",
"[ 1 -1 0 -1 0 0 0 0] [-1 1 0 -1 0 0 0 0] [1, 2, 9, 10] 1\n",
"[ 1 -1 0 -1 0 0 0 0] [-1 1 0 -1 0 0 0 0] [5, 6, 13, 14] 2\n",
"[ 1 -1 -1 -1 0 0 0 0] [-1 1 -1 -1 0 0 0 0] [1, 2, 13, 14] 1\n",
"[ 1 -1 -1 0 0 0 0 0] [ 1 1 -1 0 0 0 0 0] [1, 3, 4, 6] 1\n",
"[ 1 -1 -1 0 0 0 0 0] [ 1 1 -1 0 0 0 0 0] [9, 11, 12, 14] 2\n",
"[ 1 -1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [1, 3, 8, 10] 1\n",
"[ 1 -1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [5, 7, 12, 14] 2\n",
"[ 1 -1 -1 -1 0 0 0 0] [ 1 1 -1 -1 0 0 0 0] [1, 3, 12, 14] 1\n",
"[ 1 0 -1 -1 0 0 0 0] [-1 0 1 -1 0 0 0 0] [1, 4, 9, 12] 1\n",
"[ 1 0 -1 -1 0 0 0 0] [-1 0 1 -1 0 0 0 0] [3, 6, 11, 14] 2\n",
"[ 1 -1 -1 -1 0 0 0 0] [-1 -1 1 -1 0 0 0 0] [1, 4, 11, 14] 1\n",
"[ 1 0 -1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [1, 5, 8, 12] 1\n",
"[ 1 0 -1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [3, 7, 10, 14] 2\n",
"[ 1 -1 -1 -1 0 0 0 0] [ 1 -1 1 -1 0 0 0 0] [1, 5, 10, 14] 1\n",
"[ 1 -1 -1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [1, 6, 9, 14] 1\n",
"[ 1 -1 -1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [1, 7, 8, 14] 1\n",
"[-1 1 -1 0 0 0 0 0] [ 1 1 -1 0 0 0 0 0] [2, 3, 4, 5] 1\n",
"[-1 1 -1 0 0 0 0 0] [ 1 1 -1 0 0 0 0 0] [10, 11, 12, 13] 2\n",
"[-1 1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [2, 3, 8, 9] 1\n",
"[-1 1 0 -1 0 0 0 0] [ 1 1 0 -1 0 0 0 0] [6, 7, 12, 13] 2\n",
"[-1 1 -1 -1 0 0 0 0] [ 1 1 -1 -1 0 0 0 0] [2, 3, 12, 13] 1\n",
"[ 0 1 -1 -1 0 0 0 0] [ 0 -1 1 -1 0 0 0 0] [2, 4, 10, 12] 1\n",
"[ 0 1 -1 -1 0 0 0 0] [ 0 -1 1 -1 0 0 0 0] [3, 5, 11, 13] 2\n",
"[-1 1 -1 -1 0 0 0 0] [-1 -1 1 -1 0 0 0 0] [2, 4, 11, 13] 1\n",
"[-1 1 -1 -1 0 0 0 0] [ 1 -1 1 -1 0 0 0 0] [2, 5, 10, 13] 1\n",
"[ 0 1 -1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [2, 6, 8, 12] 1\n",
"[ 0 1 -1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [3, 7, 9, 13] 2\n",
"[-1 1 -1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [2, 6, 9, 13] 1\n",
"[-1 1 -1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [2, 7, 8, 13] 1\n",
"[ 1 1 -1 -1 0 0 0 0] [-1 -1 1 -1 0 0 0 0] [3, 4, 11, 12] 1\n",
"[ 1 1 -1 -1 0 0 0 0] [ 1 -1 1 -1 0 0 0 0] [3, 5, 10, 12] 1\n",
"[ 1 1 -1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [3, 6, 9, 12] 1\n",
"[ 1 1 -1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [3, 7, 8, 12] 1\n",
"[-1 0 1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [4, 5, 8, 9] 1\n",
"[-1 0 1 -1 0 0 0 0] [ 1 0 1 -1 0 0 0 0] [6, 7, 10, 11] 2\n",
"[-1 -1 1 -1 0 0 0 0] [ 1 -1 1 -1 0 0 0 0] [4, 5, 10, 11] 1\n",
"[ 0 -1 1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [4, 6, 8, 10] 1\n",
"[ 0 -1 1 -1 0 0 0 0] [ 0 1 1 -1 0 0 0 0] [5, 7, 9, 11] 2\n",
"[-1 -1 1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [4, 6, 9, 11] 1\n",
"[-1 -1 1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [4, 7, 8, 11] 1\n",
"[ 1 -1 1 -1 0 0 0 0] [-1 1 1 -1 0 0 0 0] [5, 6, 9, 10] 1\n",
"[ 1 -1 1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [5, 7, 8, 10] 1\n",
"[-1 1 1 -1 0 0 0 0] [ 1 1 1 -1 0 0 0 0] [6, 7, 8, 9] 1\n"
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Text
Für \(a>0\wedge b>0\) beweisen wir \( a/b+b/a\geq2\):
\(a/b+b/a<2 \Leftarrow\frac{a^2-2ab+b^2}{2ab}<0\Leftarrow\frac{(a-b)^2}{2ab}<0\)
Nun ist aber
\(\neg(\frac{(a-b)^2}{2ab}<0)\Rightarrow\neg(a/b+b/a<2)\Rightarrow a/b+b/a\geq2\)
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