What's the Correct Interpretation of |r| in Math?

[phospho]

I thought |r| means the positive values of r? Why do they say it means -1<r<1? Also, if |r| means -1<r<1 then why do they say |r|<1 when |r| is already -1<r<1 ?

 

[Mark44]

I thought |r| means the positive values of r?

No that's not what |r| means. It means all of the values of r that are within 1 unit of 0. That would include -.5, for example, not just positive values (and zero) of r.

Why do they say it means -1<r<1? Also, if |r| means -1<r<1 then why do they say |r|<1 when |r| is already -1<r<1 ?

These two statements say exactly the same thing: |r| < 1 and -1 < r < 1. They are equivalent statements.

 

[phospho]

No that's not what |r| means. It means all of the values of r that are within 1 unit of 0. That would include -.5, for example, not just positive values (and zero) of r.


These two statements say exactly the same thing: |r| < 1 and -1 < r < 1. They are equivalent statements.

|r| is it not the absolute value of r? if so then I don't understand how it can be negative.

how can they also be equivalent when they said |r| is -1<r<1 then they are saying |r|<1, which is -1<r<1 < 1?

 

[Mark44]

|r| is it not the absolute value of r?

Yes

if so then I don't understand how it can be negative.

Who is "it"? There are two things we're talking about here - r and |r|. Which one do you mean?

how can they also be equivalent when they said |r| is -1<r<1

No. I didn't say "|r| is -1<r<1".

I said that |r| < 1 (first statement) and -1 < r < 1 (second statement) were two statements that said exactly the same thing. They are equivalent statements.

then they are saying |r|<1, which is -1<r<1 < 1?

Now, who are "they"? I said that |r|<1 and -1<r<1 [STRIKE]< 1[/STRIKE] were equivalent statements

 

[Erland]

There is a typo in the hint. It should be: |r|<1 means -1<r<1.

 

[Mark44]

There is a typo in the hint. It should be: |r|<1 means -1<r<1.

To be honest, I didn't notice that. I have my browser open to less than full-screen width, and didn't notice that hint way off to the right.