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sasogeek

  • 2 years ago

what does absolute value mean?

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  1. Shadowys
    • 2 years ago
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    mathematical description or layman description?

  2. Shadowys
    • 2 years ago
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    |x| --> x if x>0, or -x if x<0

  3. sasogeek
    • 2 years ago
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    wha...? :s i'm lost

  4. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    how do u determine it?

  6. EulerGroupie
    • 2 years ago
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    Do you have an example?

  7. sasogeek
    • 2 years ago
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    find the absolute value of x

  8. EulerGroupie
    • 2 years ago
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    I liked @Shadowys 's description.

  9. EulerGroupie
    • 2 years ago
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    His mathematical description was a great answer for your question.

  10. sasogeek
    • 2 years ago
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    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?

  11. Shadowys
    • 2 years ago
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    it's the definition. the proof is the first line i gave you. the mathematical description.

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

  15. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    i don't think it's enough to settle with |x|=x, |-z|=z ...

  17. Shadowys
    • 2 years ago
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    yes. it is not.

  18. sasogeek
    • 2 years ago
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    it doesn't make sense

  19. Shadowys
    • 2 years ago
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    |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
    • 2 years ago
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    why?

  21. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    @Zarkon

  24. Shadowys
    • 2 years ago
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    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
    • 2 years ago
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    well i'm still not satisfied with the given answer.

  26. Zarkon
    • 2 years ago
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    if x<0 then x is negative...so -x is positive thus |x|=-x

  27. sasogeek
    • 2 years ago
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    @Shadowys would you say that |y+1|=y+1?

  28. Zarkon
    • 2 years ago
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    only if \(y+1\ge0\)

  29. Zarkon
    • 2 years ago
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    if \(y+1<0\) then \(|y+1|=-(y+1)\)

  30. sasogeek
    • 2 years ago
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    what's with the magnitude mentioned in the definition by google?

  31. sasogeek
    • 2 years ago
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    magnitude is distance... right?

  32. EulerGroupie
    • 2 years ago
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    From a linear geometric perspective, yes. If we are talking about pressure, for example, not really.

  33. Zarkon
    • 2 years ago
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    the absolute value of a number is its distanceto the origin

  34. sasogeek
    • 2 years ago
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    okay now this makes more sense than the earlier explanation/definition... thanks :)

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