Since, an $n$ - $tuple$ is only defined when its length i.e $n$ is non-negative and finite.
If an element of $F^{\infty}$ is of the form $(x_1,x_2,x_3,.....)$, then how can it be a defined vector space?
I know that $F^{\infty}$ satisfies the properties concerning the usual operations of vector addition and scalar multiplication.
But my doubt arised from the definition of a list of length $n$ (or an $n$ - $tuple$) as mentioned in Linear Algebra Done Right - Sheldon Axler.
I have attached the screenshots from the book to verify my doubt.
Definitions as mentioned in the book:
List of length $n$ ,
$F^{n}$ , $F^{\infty}$
