Let (E subset mathbb{R}^{d}). Show that (operatorname{dim}left(E times mathbb{R}^{n}ight)=operatorname{dim} E+n). Does a similar formula hold for (E

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Let \(E \subset \mathbb{R}^{d}\). Show that \(\operatorname{dim}\left(E \times \mathbb{R}^{n}ight)=\operatorname{dim} E+n\). Does a similar formula hold for \(E \times F\) where \(E \subset \mathbb{R}^{d}\) and \(F \subset \mathbb{R}^{n}\) ?

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