## sasogeek 2 years ago what does absolute value mean?

mathematical description or layman description?

|x| --> x if x>0, or -x if x<0

3. sasogeek

wha...? :s i'm lost

lol that's the mathematical description. in layman terms, if x is positive, like 4, then the absolute value of it is 4. if x is negative, like -5, then the absolute value of it is 5.

5. sasogeek

how do u determine it?

6. EulerGroupie

Do you have an example?

7. sasogeek

find the absolute value of x

8. EulerGroupie

9. EulerGroupie

10. sasogeek

i know if i have |x| the solution is |x|=x that i know. my question is, how do you arrive at that conclusion... proof?

it's the definition. the proof is the first line i gave you. the mathematical description.

12. EulerGroupie

It's only x if x is positive. It is -x if x is negative. It's one of those things that is so simple that it becomes tricky again. Say we are looking for |x| and x is -4... the answer is 4... but from the perspective of the original x, the answer is -(-4)=4.

13. sasogeek

google: "The magnitude of a real number without regard to its sign" i don't see that in ur description/definition/proof.... there's nothing related to magnitudes :/

14. EulerGroupie

I've never seen a more rigorous proof than the piece-wise description given by @Shadowys . The literal meaning is: distance from the origin.

i.e. that's the layman terms. also, i.e. that's in terms of vectors. |-4|-->4 |-2|-->2 |-x|-->x, for x>0

16. sasogeek

i don't think it's enough to settle with |x|=x, |-z|=z ...

yes. it is not.

18. sasogeek

it doesn't make sense

|x| --> x if x>0, or -x if x<0 this is the definition. in fact, it's called the absolute value function. that means it must be like that. MUST

20. sasogeek

why?

there is no why in this. it is defined that way. the reason you're learning this because this particular function has importance in geometrical analysis.

22. sasogeek

let's just say there is a why. there's a reason for everything, if not i could just make my own math rules and say everyone MUST follow that rule.... unless u don't know the answer to the why in this... :/

23. sasogeek

@Zarkon

yes. you can make your own rules, if they have an importance in something and if they conform to the original rules of mathematics.

25. sasogeek

well i'm still not satisfied with the given answer.

26. Zarkon

if x<0 then x is negative...so -x is positive thus |x|=-x

27. sasogeek

@Shadowys would you say that |y+1|=y+1?

28. Zarkon

only if \(y+1\ge0\)

29. Zarkon

if \(y+1<0\) then \(|y+1|=-(y+1)\)

30. sasogeek

what's with the magnitude mentioned in the definition by google?

31. sasogeek

magnitude is distance... right?

32. EulerGroupie

From a linear geometric perspective, yes. If we are talking about pressure, for example, not really.

33. Zarkon

the absolute value of a number is its distanceto the origin

34. sasogeek

okay now this makes more sense than the earlier explanation/definition... thanks :)