April 13th, 2017, 04:40 PM  #1 
Senior Member Joined: Feb 2016 From: seattle Posts: 312 Thanks: 10  absolute value but in set notation
x>=0 but as set notation I have not seen this written, is there another way other than always true, reall number symbol? thanks!! 
April 13th, 2017, 04:44 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,105 Thanks: 576 
by definition $x \geq 0$ so yes the set $\{x:x\geq 0\} = \mathbb{R}$ this does assume that $x \in \mathbb{R}$ Absolute value means something a little different for complex numbers than for reals but it is still true that $x\geq 0,~\forall x \in \mathbb{C}$ so if $x \in \mathbb{C}$ $\{x: x \geq 0 \} = \mathbb{C}$ Last edited by romsek; April 13th, 2017 at 04:46 PM. 
April 13th, 2017, 05:12 PM  #4 
Senior Member Joined: Feb 2016 From: seattle Posts: 312 Thanks: 10 
Thanks! Wanted to answer it but was worried, as did not want to end up answering it like my teacher if there was other was to answer it.

April 13th, 2017, 05:21 PM  #5 
Senior Member Joined: Feb 2016 From: seattle Posts: 312 Thanks: 10 
One of these is the way he answered it, I saw it as saying x is equal to or larger than zero. If wrong or right, I wonder why oo would be included...unless of course it's just me miss reading it, we don't have access to a better copy Last edited by GIjoefan1976; April 13th, 2017 at 05:23 PM. 
April 13th, 2017, 05:29 PM  #6 
Senior Member Joined: Feb 2016 From: Australia Posts: 967 Thanks: 344 Math Focus: Yet to find out. 
Is there something about your teachers answer that you don't understand? It looks good to me. There are many ways to show what has been shown in this question.

April 13th, 2017, 05:41 PM  #7  
Senior Member Joined: Sep 2015 From: CA Posts: 1,105 Thanks: 576  Quote:
$x = \begin{cases}x &x<0 \\\phantom{}0 &x=0 \\ \phantom{}x &x>0 \end{cases}$ so $\infty = \infty > 0$ thus it would be included.  
April 13th, 2017, 05:46 PM  #8 
Senior Member Joined: Feb 2016 From: seattle Posts: 312 Thanks: 10  Thanks, yes I am unsure of why negative infinity would be included since that's smaller than 0 I thought we wanted all real numbers and they had to be positive since we can't have a negative absolute value?

April 13th, 2017, 05:47 PM  #9 
Senior Member Joined: Aug 2012 Posts: 1,143 Thanks: 249  I strongly disagree with this. $\infty \notin \mathbb R$ and $\lvert \cdot \rvert$ is not defined on the extended reals. <minor rant> And while I'm at it, y'all are raising my blood pressure writing $\{x : \text{foo}\}$, leading yet another generation of students to be confused about unrestricted comprehension. This includes the tutorial linked earlier in this thread which starts off with this erroneous example. Frege and Russell had this conversation over a century ago, let's all learn something from it. </minor rant> Last edited by Maschke; April 13th, 2017 at 06:00 PM. 
April 13th, 2017, 05:48 PM  #10  
Senior Member Joined: Sep 2015 From: CA Posts: 1,105 Thanks: 576  Quote:
I'm speaking within the context of this problem to a student grappling with the concept of absolute value. This is not the place to discuss whether or not infinity is a real number or not.  

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