I was thinking this: If I have the set [itex] A = \{ \mathbb{R}^n, \mathbb{R}^n \} [/itex] where for the "first" element I mean the real vector space [itex] \mathbb{R}^n [/itex], and the "second" element is the additive group [itex] \mathbb{R}^n [/itex], then does the set [itex] A [/itex] contain one element ([itex] \mathbb{R}^n [/itex])? Or it contains two elements (a vector space and a group)?(adsbygoogle = window.adsbygoogle || []).push({});

Maybe this has something to do with category theory, where one considers not only the sets but the structure defined on them. But as sets both have the same elements, so I am confused if it has two elements or just one.

Thanks.

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# Set with a vector space an a group

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