Math Is Fun Forum

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

meo_beo

Member

Registered: 2008-06-01

Posts: 4

Re: Nested absolute value in algebraic expression

I think you got it right.

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

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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.

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"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..."

Maracuya

Member

Registered: 2008-02-02

Posts: 12

Re: Nested absolute value in algebraic expression

To meo_beo , Ricky, aleclarsen12 thanks  for the replies.

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

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

Maracuya

Member

Registered: 2008-02-02

Posts: 12

Re: Nested absolute value in algebraic expression