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Combined with the result of Simons, this shows that the analogue of
Bernstein's theorem is true in dimensions up to 8, and false in higher dimensions.
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340:{\displaystyle \{x\in \mathbb {R} ^{8}:x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}=x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2}\}}
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Furthermore, this particular problem has an additional difficulty: The graph of a real-valued function defined on
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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In order to make this clear, the words "up through" should be used. And then just to make it
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And please note that the example cited in the above quote from the article
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does not specify whether the integer n is included or excluded.
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The article's summary of final results is as follows:
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is not expressed in terms of the graph of a function
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