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#1 2008-06-01 15:09:18

Maracuya
Member
Registered: 2008-02-02
Posts: 12

Nested absolute value in algebraic expression

Please help me get this straight.

I need to express this with "at least one less pair of absolute value signs."

Since 

,  the expression inside the parenthesis must be negative or zero.

So have I got it, or am I missing something important.?

Thanks

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#2 2008-06-01 15:19:30

meo_beo
Member
Registered: 2008-06-01
Posts: 4

Re: Nested absolute value in algebraic expression

I think you got it right.

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#3 2008-06-01 15:25:53

aleclarsen12
Member
Registered: 2008-06-01
Posts: 36

Re: Nested absolute value in algebraic expression

the technical definition of "absolute value" is:
|x|=√x²

Because a negative squared is a positive sqrt. is then positive (on its first solution of coarse)

So it is realy:

Unfortunately my 7th grade mind know not how to simplify


Twitter: http://twitter.com/AlecBeta
Blog: http://AlecBeta.us.to

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#4 2008-06-01 16:11:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Nested absolute value in algebraic expression

Maracuya, you are right.

aleclarsen12, while that is a technically correct definition, it also tends to be very difficult to work with.  Stick to the more intuitive (piecewise) definition of absolute value, in general.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2008-06-01 17:54:57

Maracuya
Member
Registered: 2008-02-02
Posts: 12

Re: Nested absolute value in algebraic expression

To meo_beo , Ricky, aleclarsen12 thanks  for the replies. smile

To :aleclarsen12 , I'm sure Ricky gave you good advice.  But...

here's a problem for you where your definition will make a problem much simpler, while the piecewise definition that I gave will make your life hard!

Try to prove this fact :

This is from a college level book, so tell me if you want more hints.

Maracuya

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#6 2008-06-01 18:34:48

Dragonshade
Member
Registered: 2008-01-16
Posts: 147

Re: Nested absolute value in algebraic expression

Can I prove it like this
Consider, a, b two vectors

|a+b| is the length of the 3rd side of triangle consisted of a and b

|a| ,|b| are length of side a and side b

sum of two sides always larger than the other one
and when the two vectors are parallel they equal

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#7 2008-06-01 19:16:44

Maracuya
Member
Registered: 2008-02-02
Posts: 12

Re: Nested absolute value in algebraic expression

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