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When is Modulus Negative !

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by The Recruit » Mon Aug 08, 2011 12:47 am
Hello Everyone,

This is very basic, but i still wanted to get it cleared.

Q: When is modulus of a number negative, i know that only when x<0 ,

so that means |-3|=3 ? cant be right

so, someone please explain that what are the cases in which |x|=-x [ yes, only if x<0 but how :) ]

Thanks a tonne for replying , kind souls !
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by Anurag@Gurome » Mon Aug 08, 2011 12:53 am
The Recruit wrote:Hello Everyone,

This is very basic, but i still wanted to get it cleared.

Q: When is modulus of a number negative, i know that only when x<0 ,

so that means |-3|=3 ? cant be right

so, someone please explain that what are the cases in which |x|=-x [ yes, only if x<0 but how :) ]

Thanks a tonne for replying , kind souls !
That's some serious misconception!
Modulus or absolute value of a number is never negative.

Absolute value of any number x is defined as,
  • 1. |x| = x for x ≥ 0
    2. |x| = -x for x < 0
Hence, for x < 0, |x| = -x which is greater than zero as x itself is negative.

Hope that clears your confusion.
Anurag Mairal, Ph.D., MBA
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by The Recruit » Mon Aug 08, 2011 1:03 am
Thanks for the prompt reply Anurag,

so if u'stand correct, Based on |x| = -x for x < 0

|-3| = - 3 as -3<0, but thats not correct !

Thanks for clearing
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by The Recruit » Mon Aug 08, 2011 2:02 am
Anyone ?
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by Anurag@Gurome » Mon Aug 08, 2011 5:51 am
The Recruit wrote:Thanks for the prompt reply Anurag,

so if u'stand correct, Based on |x| = -x for x < 0

|-3| = - 3 as -3<0, but thats not correct !

Thanks for clearing
For x < 0, |x| = -x
In this case, x = -3
Hence, |x| = -x = -(-3) = 3

Thus, |-3| = 3

Hope that helps.
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