November 25th, 2012, 03:10 AM  #1 
Member Joined: Nov 2009 Posts: 90 Thanks: 0  Notation ? and ?
I'm trying to learn some formal language. Say we have a function y=f(x)=2x. Then I want to say as efficiently and clearly as possible that for any x in the set of real numbers, there is one and only one y, also in the set of real numbers. I don't know the correct syntax and punctuation and perhaps I even misunderstood some symbol. Can I write ? Thanks! 
November 25th, 2012, 06:39 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Notation ? and ?
To express uniqueness using this notation, you need something like the following: For every real number x, there exists a real number y such that [(y has a certain property) and (for all real z, if z has this property, z = y)] 
November 25th, 2012, 07:33 AM  #3 
Member Joined: Nov 2009 Posts: 90 Thanks: 0  Re: Notation ? and ?
Thank you for your reply, but I'm having trouble making sense of it. For every real number x there exists a real number y such that (y has a certain property) and (for all real z, if z has this property, z = y) So, putting it all together, which to me just looks like a mess. What am I missing? I don't have to define the function with predicate logic by the way. I just want to say that given any x, there is one and only one y. Thanks! 
November 25th, 2012, 09:36 AM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Notation ? and ?
There may be other ways, but that is how I would write it (and have, in submitted exercises)!


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