why $\mathbb Z[\sqrt 2] \ncong \mathbb Z[\sqrt 3]$?

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Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set

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limit laws:$\lim_{n\to\infty}\max(a_n,b_n)=\max(\lim_{n\to\infty}a_n,\lim_{n\to\infty}b_n)$

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