what does absolute value mean?

- sasogeek

what does absolute value mean?

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- schrodinger

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- anonymous

mathematical description or layman description?

- anonymous

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

- sasogeek

wha...? :s i'm lost

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## More answers

- anonymous

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.

- sasogeek

how do u determine it?

- anonymous

Do you have an example?

- sasogeek

find the absolute value of x

- anonymous

I liked @Shadowys 's description.

- anonymous

His mathematical description was a great answer for your question.

- 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?

- anonymous

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

- anonymous

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.

- 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 :/

- anonymous

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

- anonymous

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

- sasogeek

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

- anonymous

yes. it is not.

- sasogeek

it doesn't make sense

- anonymous

|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

- sasogeek

why?

- anonymous

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.

- 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... :/

- sasogeek

@Zarkon

- anonymous

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

- sasogeek

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

- Zarkon

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

- sasogeek

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

- Zarkon

only if \(y+1\ge0\)

- Zarkon

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

- sasogeek

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

- sasogeek

magnitude is distance... right?

- anonymous

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

- Zarkon

the absolute value of a number is its distanceto the origin

- sasogeek

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

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