1. Jan 10, 2015 #1

   PsychonautQQ

   

   Okay, so if r,s are elements of R and rs = 0 then either r or s has to equal zero.
   
   I'm just confused because it seems that if rs = 0 then we can show that both r and s must be zero.... I don't know what i'm doing wrong..
   
   rs = 0
   r^-1(rs) = r^-1(0) = 0
   1s = 0
   s = 0
   
   and then:
   
   rs = 0
   r(ss^-1) = (0)s^-1 = 0
   r1 = 0 = 0
   r = 0
   
   I mean, both r and s have multiplicative inverses so it seems like r and s both need to be zero by this logic.. what am i doing wrong here?

    

   PsychonautQQ, Jan 10, 2015
2. 
   Phys.org - latest science and technology news stories on Phys.org

   • • Game over? Computer beats human champ in ancient Chinese game
   • • Simplifying solar cells with a new mix of materials
   • • Imaged 'jets' reveal cerium's post-shock inner strength
3. Jan 10, 2015 #2

   mfb

   

   Insights Author

   2016 Award

   Staff: Mentor

   Not if they are zero.
   
   5*0=0 in the real numbers
   Now try to apply your prove to show 5=0. It won't work.

    

   mfb, Jan 10, 2015
4. Jan 15, 2015 #3

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   You are assuming, when you write this, that r has an inverse. Which is only true if r is not 0.
   

   So what you have proved is "if r is not 0 then s is 0"
   
   

   again, you have proved that "if s is not 0 then r is 0".
   
   

   no, this is not true.

    

   HallsofIvy, Jan 15, 2015

• Log in with Facebook
• Log in with Twitter

Your name or email address:

Do you already have an account?

• No, create an account now.
• Yes, my password is:
• Forgot your password?

Stay logged in