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### Basis of infinite Vector Space $\mathbb R^{\infty}$ [duplicate]

I have a question about one example in Linear Algebra. Let $\mathbb R^∞$ be the vector space of infinite sequences $(\alpha_1, \alpha_2, \alpha_3, \ldots )$ of real numbers. Scalar multiplication ...
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### Basis for $\mathbb{R}^{\infty}$ [duplicate]

It follows from Zorn's Lemma that every vector space $V$ has a basis (this means, a subset $B$ of $V$ that generate any $v \in V$ by means a finite linear combination, and such that $B$ is LI) . But, ...
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### Can we reproduce a basis of a vector space of all sequences? [duplicate]

Can we reproduce a basis of a vector space of all sequences?(if exists since by every vector space has a basis, but can we reproduce it)
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### Basis of $\mathbb{F}[[x]]$ over $\mathbb{F}$ without AC
Does the ring of formal power series $\mathbb{F}[[x]]$ as a vector space over $\mathbb{F}$ admit a basis without assuming the Axiom of choice, at least in some special cases of $\mathbb{F}$? I'm ...
### basis for $\mathbb{R}^{\mathbb{N}}:=\left\{f:\mathbb{N}\to\mathbb{R}\right\}$, and its cardinality.
I know that all vector space has a basis. My question is "concrete" example for basis for $\mathbb{R}$-vector space $\mathbb{R}^{\mathbb{N}}:=\left\{f:\mathbb{N}\to\mathbb{R}\right\}$. If I refer ...