I thought the definition of a field was the set of all real numbers plus addition and multiplication (or whatever the particular set of operations are) and since its elements have no direction, by definition, they are not vectors; thus cannot be a vector space.(adsbygoogle = window.adsbygoogle || []).push({});

(1) Am I wrong?

(2) Can a field be a vector space?

(3) Does the following statement make sense?

A field is a vector space over itself with dimension 1.

(4) Can a field have a subspace? (I thought subfields are to fields as subspaces are to vector spaces.

Thanks!

Joe

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# I need an authoritative answer

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