| 31. | The hypotheses of Goursat's theorem can be weakened significantly.
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| 32. | Both orders divide 8, as predicted by Lagrange's theorem.
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| 33. | This is the seed idea generalized in Noether's theorem.
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| 34. | Therefore, the original Sperner lemma follows from Musin's theorem.
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| 35. | Using Taylor's theorem, we can write at every iteration:
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| 36. | Liouville's theorem is a classical theorem of conformal geometry.
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| 37. | In fact, it was Cauchy who proved Liouville's theorem.
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| 38. | The name derives from Abel's theorem on power series.
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| 39. | Start with the left side of Green's theorem:
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| 40. | Stone's theorem has numerous applications in quantum mechanics.
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