Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Real numbers

  1. Apr 4, 2006 #1
    i know that the set "all real numbers" make up a vector space, but how do you prove that it is so?
     
  2. jcsd
  3. Apr 4, 2006 #2
  4. Apr 4, 2006 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook