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linear algebra – Existence of area with uncountably innumerable foundation components and Cayley desk equal to Cayley-Dickson for $e_n, quad n in mathbb{N}$ Answer

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linear algebra – Existence of area with uncountably innumerable foundation components and Cayley desk equal to Cayley-Dickson for $e_n, quad n in mathbb{N}$

I’m trying to discover a area with foundation components $e_i forall iin mathbb{R}$ which, for $i in mathbb{N}$, has a Cayley desk equal to the Cayley-Dickson desk, which has ties to the analytic XOR.

Is there a route of proving or disproving the actuality of this figure? There are definitely areas with uncountably innumerable foundation components. This is utilizing ZFC.

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