I'm fairly certain the following is a vector space isomorphism [tex]\phi :\mathbb{R}^\infty\rightarrow\mathbb{R}^\infty[/tex] where the vector space is the space of infinite sequences of real numbers and phi is defined by [tex] \phi(a_1,a_2,...)=(0,a_1,a_2,...) [/tex]. The mapping is linear and the inverse seems to be well defined. Is my logic flawed?(adsbygoogle = window.adsbygoogle || []).push({});

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# Isomorphism between R^inf and a proper subset of R^inf

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