Question

what does absolute value mean?

Answer 1

mathematical description or layman description?

Answer 2

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

Answer 3

wha...? :s i'm lost

Answer 4

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.

Answer 5

how do u determine it?

Answer 6

Do you have an example?

Answer 7

find the absolute value of x

Answer 8

I liked @Shadowys 's description.

Answer 9

His mathematical description was a great answer for your question.

Answer 10

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?

Answer 11

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

Answer 12

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.

Answer 13

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 :/

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

yes. it is not.

Answer 18

it doesn't make sense

Answer 19

|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

Answer 20

why?

Answer 21

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.

Answer 22

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... :/

Answer 23

@Zarkon

Answer 24

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

Answer 25

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

Answer 26

if x<0 then x is negative...so -x is positive

thus |x|=-x

Answer 27

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

Answer 28

only if \(y+1\ge0\)

Answer 29

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

Answer 30

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

Answer 31

magnitude is distance... right?

Answer 32

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

Answer 33

the absolute value of a number is its distanceto the origin

Answer 34

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