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mathematical description or layman description?
|x| --> x if x>0, or -x if x<0
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.
how do u determine it?
Do you have an example?
find the absolute value of x
I liked @Shadowys 's description.
His mathematical description was a great answer for your question.
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.
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.
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 :/
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
i don't think it's enough to settle with |x|=x, |-z|=z ...
yes. it is not.
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
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.
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... :/
yes. you can make your own rules, if they have an importance in something and if they conform to the original rules of mathematics.
well i'm still not satisfied with the given answer.
if x<0 then x is negative...so -x is positive thus |x|=-x
@Shadowys would you say that |y+1|=y+1?
only if \(y+1\ge0\)
if \(y+1<0\) then \(|y+1|=-(y+1)\)
what's with the magnitude mentioned in the definition by google?
magnitude is distance... right?
From a linear geometric perspective, yes. If we are talking about pressure, for example, not really.
the absolute value of a number is its distanceto the origin
okay now this makes more sense than the earlier explanation/definition... thanks :)