query: What is the need to include the "additive identity exists" axiom in the set of vector space axioms?
positive_passages.docid: 141833
positive_passages.text: Is it possible to construct a quasi-vectorial space without an identity element?
negative_passages.docid: 46875
negative_passages.text: The identity morphism in $\mathbf{Set}$ is the identity function
negative_passages.docid: 151117
negative_passages.text: Are all fields vector spaces?
negative_passages.docid: 45958
negative_passages.text: Proof that the Euler characteristic is additive
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 140190
negative_passages.text: Binary operation $xy$, has identity, but not associativity. Is the inverse unique?
negative_passages.docid: 132532
negative_passages.text: Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
negative_passages.docid: 54497
negative_passages.text: Set Notation - Inclusion and Proper Inclusion
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 129810
negative_passages.text: What kind of vector spaces have exactly one basis?
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 5313
negative_passages.text: Existence of how many sets is asserted by the axiom of choice in this case?
negative_passages.docid: 146188
negative_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
negative_passages.docid: 123408
negative_passages.text: Why a subspace of a vector space is useful
negative_passages.docid: 34674
negative_passages.text: Does the proof of Bolzano-Weierstrass theorem require axiom of choice?
negative_passages.docid: 72952
negative_passages.text: Uniqueness of a linear map on a basis of a vector space
negative_passages.docid: 127664
negative_passages.text: Inverse elements in the absence of identities/associativity.