# cardinality of the projective limit of direct sum of powers of the rationals

$\mathrm{Card}\left[\mathrm{Aut} \left(\bigoplus_{n=1}^{\infty} \mathbb{Q}^{n}\right)\right] \cong \mathrm{Card}(\mathrm{Aut} (\mathbb{R}^\mathbb{R}))$