# Real numbers

1. Apr 4, 2006

### asdf1

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

2. Apr 4, 2006

3. Apr 4, 2006

### 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.