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January 23rd, 2013, 08:52 PM  #1 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  What is \mathbb{R}\{1\}?
I have been asked to help a friend with his homework. He has questions, but no textbook, so I can't look up what symbols mean. The question is Show that is a group under the operation What is ? Is it all reals except for negative one? If yes, how on earth do I prove that it's a group? Thanks. 
January 23rd, 2013, 09:25 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: What is \mathbb{R}\{1\}?
That is a standard interpretation of the symbols. You prove something is a group by... Wait for it... The DEFINITION! Closed under operation "*" Has identity Has inverse Associative 
January 23rd, 2013, 10:11 PM  #3  
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Re: What is \mathbb{R}\{1\}? Quote:
 
January 23rd, 2013, 10:13 PM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: What is \mathbb{R}\{1\}?
So what's the inverse of element "c"?

January 23rd, 2013, 10:29 PM  #5  
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Re: What is \mathbb{R}\{1\}? Quote:
 
January 23rd, 2013, 11:53 PM  #6 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88  Re: What is \mathbb{R}\{1\}?
in fact, ?:R{0}>R{1} given by ?(x) = x1 is a group isomorphism, since: ?(xy) = xy  1 = xy + x  x + y  y  1 = xy  x  y + 1 + (x1) + (y1) = (x1)(y1) + (x1) + (y1) = (x1)*(y1) = ?(x)*?(y). this gives us a way to find c^1: it is: ?(1/(?^1(c))) = ?(1/(c+1)) = 1/(c+1)  1 