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[itex]$\mathbf{F}$^{\infty}[/itex] is the vector space consisting of all sequences of elements of [itex]$\mathbf{F}$[/itex], and [itex]$\mathbf{F}$[/itex] denotes the real or complex numbers.

I was thinking of showing that no list spans [itex]$\mathbf{F}$^{\infty}[/itex], which would mean that it had no basis and therefore could not be finite dimensional.

I'm just not sure if this aproach works, and I'm also a little fuzzy on how to show this.

Another idea I had was to assume that [itex]$\mathbf{F}$^{\infty}[/itex]was finite dimensional and show a contradiction, but again I am unsure of how to actually show this.

Any ideas or input would be much appreciated !