Elem lin algebra (Vector space question)

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The discussion centers on the definition of a vector space and the role of the additive identity. It questions how a space can be considered a vector space without a zero vector, proposing that if a vector e satisfies x + e = x for any vector x, then e acts as the zero vector. The conversation clarifies that in this specific vector space, e is not (0,0) but rather (1,0). This leads to the conclusion that (1,0) serves as the additive identity for this vector space. Understanding the nature of e is crucial for defining the vector space accurately.
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How is the following a vector space if it does not have a zero vector?
 

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If the space has a vector e such that x + e = x, for any vector x in the space, then e is acting as the zero vector. More formally, e is the additive identity.
 
but e = (0,0) is not of the form (1,x)
 
Miike012 said:
but e = (0,0) is not of the form (1,x)

But for this vector space, e ≠ (0, 0).

What is e for this vector space?
 
is it (1,0)?
 
Miike012 said:
is it (1,0)?
Yes, that's e .
 

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