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November 25th, 2012, 03:10 AM   #1
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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!
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November 25th, 2012, 06:39 AM   #2
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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)]
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November 25th, 2012, 07:33 AM   #3
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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!
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November 25th, 2012, 09:36 AM   #4
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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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