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

Subfield of the field of complex numbers

  1. Feb 6, 2010 #1
    Can anyone prove to me why each subfield of the field of complex numbers contains every rational numers?
    Last edited: Feb 6, 2010
  2. jcsd
  3. Feb 6, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Hrm. Let's start with a simpler question: can you say why they must all contain the number 2? What other numbers can you say something about?
  4. Feb 6, 2010 #3


    User Avatar
    Science Advisor

    Any subfield of the complex numbers must include 0 and 1. Since it is closed under addition, it must include every positive integer. Since it has additive inverses, it must include every negative integer. Since every member except 0 has a multiplicative inverse, ....
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook