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Answer by Will Brian for Can you partition the sphere into orthonormal bases?

Using the Axiom of Choice, yes you can.To get such a partition, start by enumerating all the points of the sphere with order type $\mathfrak{c}$ (the least ordinal number with the same cardinality as...

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Can you partition the sphere into orthonormal bases?

I've been writing some linear algebra problems with colleagues, and the following question occurred to us:Let $S^2$ denote the unit sphere in $\mathbb{R}^3$. Does there exist apartition...

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