# Stupid Math Question: Absolute Values **URL:** \ **Category:** Factual Questions\ **Created:** [February 23, 2003, 4:16am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910 "2003-02-23T04:16:24Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [February 23, 2003, 4:16am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/1 "2003-02-23T04:16:24Z")
First, what is the solution to: | a-b | = | (a-b)| = a-b, correct? So, then what’s the solution to: |-a-b| = |(-a-b)| = | -1\*(a+b)| = |-(a+b)| = a+b, correct? or no? Just a little rusty…thanks! - Jinx ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 23, 2003, 4:19am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/2 "2003-02-23T04:19:38Z")
Both depend on the values of a and b. The first could be a-b or b-a, whichever is nonnegative. The second could be -a-b or a+b, again, whichever is nonnegative. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 23, 2003, 4:28am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/3 "2003-02-23T04:28:31Z")
Both depend on the values of a and b. The first could be a-b or b-a, whichever is nonnegative. The second could be -a-b or a+b, again, whichever is nonnegative. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [February 23, 2003, 4:40am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/4 "2003-02-23T04:40:16Z")
Hmm, so Cabbage, would you say that we cannot even say that | -X | = X ? - Jinx ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [February 23, 2003, 4:48am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/5 "2003-02-23T04:48:10Z")
That’s correct. For example, if x = -1, then we have |x| = -x = -(-1) = 1. In the past, this has caused some of my calculus students no end of frustration–they get confused when they see that sometimes |x| = -x; they don’t expect a negative sign there. In general, |x| is defined to be: 1. |x| = x, if x \>= 0 2. |x| = -x, if x \< 0. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 23, 2003, 4:50am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/6 "2003-02-23T04:50:53Z")
No, |-X| = X always. But in the case |a-b| it depends on whether a \> b or not. For example, |3-5] = |-2| = 2 = b-a, but |5-3| = |2| = 2 = a-b. ---
**Author:** ![Cubsfan](https://avatars.discourse-cdn.com/v4/letter/c/f4b2a3/32.png) [@Cubsfan](https://boards.straightdope.com/u/Cubsfan)\ **Post date:** [February 23, 2003, 4:51am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/7 "2003-02-23T04:51:10Z")
> [@](#): > > \*Originally posted by Jinx \* > \*_First, what is the solution to: | a-b | = | (a-b)| = a-b, correct? > So, then what’s the solution to: > |-a-b| = |(-a-b)| = | -1_(a+b)| = |-(a+b)| = a+b, correct? or no? > > Just a little rusty…thanks! > > - Jinx \*\* |a-b| does not equal a-b for any value of b greater than a. You are differentiating between |a-b| and |(a-b)| when they are literally the same thing. Same for |-a-b| and |(-a-b)|. If b less than -a then the second one does not hold true. As was said above, it all depends on the values in that you use. ---
**Author:** ![vasyachkin](https://avatars.discourse-cdn.com/v4/letter/v/c5a1d2/32.png) [@vasyachkin](https://boards.straightdope.com/u/vasyachkin)\ **Post date:** [February 23, 2003, 4:52am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/8 "2003-02-23T04:52:06Z")
what would be the point of absolute value if you could just get rid of it whenever you wanted ? you can’t get rid of it until you know the sign of the stuff you’re looking at. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 23, 2003, 4:52am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/9 "2003-02-23T04:52:18Z")
Oops…I retract that |X| = X part. It’s either X or -X, whichever is positive. ---
**Author:** ![Cubsfan](https://avatars.discourse-cdn.com/v4/letter/c/f4b2a3/32.png) [@Cubsfan](https://boards.straightdope.com/u/Cubsfan)\ **Post date:** [February 23, 2003, 4:53am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/10 "2003-02-23T04:53:03Z")
> [@](#): > > \*Originally posted by Q.E.D. \* > \*\*No, |-X| = X always. \*\* Not true. IF X=-1 then |-X| != X. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 23, 2003, 4:55am UTC](https://boards.straightdope.com/t/stupid-math-question-absolute-values/156910/11 "2003-02-23T04:55:12Z")
I know, I addressd that already. Preview is our friend.