July 7th, 2018, 04:08 PM  #11 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  
July 7th, 2018, 04:17 PM  #12 
Senior Member Joined: Aug 2012 Posts: 2,386 Thanks: 746  
July 7th, 2018, 07:20 PM  #13 
Senior Member Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402  
July 7th, 2018, 08:53 PM  #14 
Senior Member Joined: Aug 2012 Posts: 2,386 Thanks: 746  Sorry. Trying to think about 0 = 1 makes my head hurt. It turns out, by the way, that there's a thing called "the field with one element." Such a thing does not exist; but many abstract areas of math act as if it "should" exist. I don't really understand much about this but here it is. https://en.wikipedia.org/wiki/Field_with_one_element This is a pretty good article. It gives the flavor of this amazing outthere stuff whether or not you follow the details. Nobody can construct or even define a field with one element, but if they had one it would do all kinds of great things, even perhaps solve the Riemann hypothesis. Last edited by Maschke; July 7th, 2018 at 09:00 PM. 
July 8th, 2018, 12:50 PM  #15 
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723  I guess I overdid it. $x\times 1=x, x\times 0=0$. Both will be true only if $x=0$. I don't think much is done with a field consisting of one element .


Tags 
field 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
does cyclic field implies Galois field  rayman  Abstract Algebra  1  March 11th, 2014 03:27 PM 
Fin. gen field extension > intermediate field f.g. also?  watson  Abstract Algebra  1  September 20th, 2012 06:53 PM 
Show R (comm. domain) over a field k is a field if dimR<inft  watson  Abstract Algebra  1  September 14th, 2012 09:07 PM 
Every quadratic field is contained in a cyclotomic field  brunojo  Abstract Algebra  0  June 5th, 2009 06:25 PM 
field  goodfeeling  Algebra  0  December 31st, 1969 04:00 PM 