query: Any infinite dimensional vector space has a basis?
positive_passages.docid: 152742
positive_passages.text: Finding a basis of an infinite-dimensional vector space?
negative_passages.docid: 58447
negative_passages.text: Is axiom of choice required for there to be an infinite linearly independent set in a (non-finite-dimensional) vector space?
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 94929
negative_passages.text: Proof that the all bases of a subspace V consist of the same number of vectors?
negative_passages.docid: 120535
negative_passages.text: Basis of the polynomial vector space
negative_passages.docid: 112548
negative_passages.text: Existence of non-trivial linear functional on any vector space
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 69766
negative_passages.text: Is every normed vector space, an inner product space
negative_passages.docid: 69206
negative_passages.text: A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
negative_passages.docid: 9295
negative_passages.text: Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 43814
negative_passages.text: What does it mean when a set is said to be a "finitely generated vector space"?
negative_passages.docid: 133711
negative_passages.text: Orthogonal basis for infinite-dimensional vector spaces
negative_passages.docid: 87692
negative_passages.text: Basis and dimension of vector space
negative_passages.docid: 47015
negative_passages.text: Vector Space Structures over ($\mathbb{R}$,+)
negative_passages.docid: 26497
negative_passages.text: Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
negative_passages.docid: 17495
negative_passages.text: Show that the vector space of all continuous real-valued functions is infinite-dimensional