Empty Set $\{\}$ is the Only Basis of the Zero Vector Space $\{0\}$ Question
Suppose we want to find a basis for the vector space $\{0\}$. 
I know that the answer is that the only basis is the empty set.
Is this answer a definition itself or it is a result of the definitions for linearly independent/dependent sets and Spanning/Generating sets? If it is a result then would you mind mentioning the definitions of bold items which based on them this answer can be deduced.

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Link 1, Link 2, Link 3, Link 4, Link 5, Link 6

A basis has several equivalent definitions. One of which is:


*

*A basis of a vector space is a minimal generating set


So keeping that in mind, if we look at $V = \{0\}$, the only non-empty subset of this vector space is $B = \{0\}$. This set $B$ is a linearly dependent set  and thus it cannot be a basis.We make a note here that $B$ is a generating set of $V$. We know by existence of basis of a vector space that $V$ must also have a basis. So if a basis were to exist it should be a subset of $B$. As removing a linearly dependent element from a generating set does not change the span of that set, $\phi$ is a generating set.
Now the definition of a linearly dependent set in crude language is: In a vector space $V$, a subset $A$ of $V$ is said to be linearly dependent if there exists an element which can be written as a finite linear combination of the rest of the elements.
So, consider the set $\phi$; there does not exist any element in it which can be written as a finite linear combination of the other elements, hence it is not a linearly dependent set and therefore it is linearly independent.
Therefor we see that $\phi$ is a linearly independent and generates $V$ and hence a basis.
