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Given an a algebraic sequentially limit Cauchy complete Archimedean ordered field $\mathrm{F\mathbb{R}}$ F \mathbb{R}, an algebraic real limit Clifford algebra is a $\mathrm{F\mathbb{R}}$ F \mathbb{R}-Clifford algebra.
algebraic sequentially limit Cauchy complete Archimedean ordered field
algebraic limit vector space?real vector space
algebraic limit geometric algebra?real geometric algebra