Proving Vector Space of All Real Numbers

[asdf1]

i know that the set "all real numbers" make up a vector space, but how do you prove that it is so?

 

[Hammie]

I would think that you would have to show that vector addition and scalar multiplication are defined on the set, subject to conditions.

Look here:

http://www.math.niu.edu/~beachy/courses/240/vectorspace.html

 

[matt grime]

Over what field...

add up two real numbers, get a real number, multiply a real number by a real number get a real number, has a zero vector, therefore it's a vector space, over R, obviously 1-dimensional.

Equally obviously it is therefore a vector space over any subfield of R, not necessarily 1-d.