I'm learning about rings, fields, vector spaces and so forth.(adsbygoogle = window.adsbygoogle || []).push({});

The book I have states:

"Real-valued functions on R^n, denoted F(R^n), form a vector space over R. The vectors can be thought of as functions of n arguments,

f(x) = f(x_1, x_2, ... x_n) "

It then says later that these vectors cannot be specified by a finite number of scalars and so the space is infinite-dimensional. Am I missing something here? From what I see, there are only a finite number of elements x_n in the vector, so why is the space infinite-dimensional?

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# Infinite-dimensional vector space question

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