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Question related to Absolute Value

  • #1
Hi everyone;
I've got this question concerning absolute value, although I understand the concept of absolute value, I can't quite understand why option B is bigger than option A.
I would really appreciate some explanation on the following question:
I am trying to post it in Latex, but in case that the comparison is not properly viewed, here is how it goes:
Option A
(everything inside absolute value symbol, the two vertical lines), sqrt2 - 1
Option B
(everything inside absolute value symbol, the two vertical lines)
1/2 - 1

I am getting very confused with something that appears to be simple and basic enough, do I need to review some other concepts? arithmetic and/or number properties? if so can someone pin point me to some web based explanations.
Thanks
And cheers to everyone
 

Answers and Replies

  • #2
811
6
Huh? Are you asking whether

abs(sqrt(2) - 1) < abs(1/2 - 1)

Isn't it obvious?

If you can accept that sqrt(2) is a real between 1.41 and 1.42, you can see that

sqrt(2) - 1 < 1/2
sqrt(2) - 1 < abs(1/2 - 1)
abs(sqrt(2) - 1) < abs(1/2 - 1)
 
  • #3
Huh? Are you asking whether

abs(sqrt(2) - 1) < abs(1/2 - 1)

Isn't it obvious?

If you can accept that sqrt(2) is a real between 1.41 and 1.42, you can see that

sqrt(2) - 1 < 1/2
sqrt(2) - 1 < abs(1/2 - 1)
abs(sqrt(2) - 1) < abs(1/2 - 1)
Excuse me....
First I signed to this forum to get help in a proper and educated way.
Secondly I ask that question because I have a doubt related to the concept.
I already know that 1.41 or 1.42 - 1 equals 0.41 or 0.42 I also know that 0.5 - 1 equals - 0.5
and I also know that the absolute value of a number is the value of a real number regarding the sign. that's why I ask that question, there's no need to be petulant, arrogant and/or try to belittle people here Tic-Tac...
Is been 20 years ago that I saw basic Algebra and I am trying to go back to school, so please have a little more of respect.
Plus your answer, doesn't help me at all from the conceptual point.
 
  • #4
811
6
The absolute value is a function it's defined like this:

abs(x) = x, when x >= 0
abs(x) = -x, otherwise

You can calculate the right hand side in a straightforward way:

1/2 -1 = -1/2, so that means
abs(1/2 - 1) = -(-1/2) = 1/2

The right hand side is tricky because of the square root. But since we're dealing with inequalities and not interested in the exact number, we can abuse the fact that 1.41 < sqrt(2) < 1.42:

1.41 < sqrt(2) < 1.42
0.41 < sqrt(2) - 1 < 0.42

Since sqrt(2) - 1 is positive, it is equal to its own absolute value:

abs(sqrt(2) - 1) = sqrt(2) - 1, so
0.41 < abs(sqrt(2) - 1) < 0.42

And finally, since 0.42 < 1/2, we have

abs(sqrt(2) - 1) < 0.42 < 1/2, and
abs(sqrt(2) - 1) < abs(1/2 - 1)

What steps do you get stuck on? What conceptual difficulties do you have over the absolute value function?
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
249
I've got this question concerning absolute value, although I understand the concept of absolute value, I can't quite understand why option B is bigger than option A.

Option A
(everything inside absolute value symbol, the two vertical lines), sqrt2 - 1
Option B
(everything inside absolute value symbol, the two vertical lines)
1/2 - 1
I already know that 1.41 or 1.42 - 1 equals 0.41 or 0.42 I also know that 0.5 - 1 equals - 0.5
and I also know that the absolute value of a number is the value of a real number regarding the sign. that's why I ask that question
Sorry, confusedabout, but it's not at all clear what you're asking about.

You seem to be asking about why |√2 - 1| < |1/2 - 1|.

You accept that it obviously is, but you're not telling us why the obvious answer is bothering you. :confused:

As Tac-Tics :smile: says, what steps do you get stuck on? What conceptual difficulties do you have over the absolute value function?
 
  • #6
33,162
4,847
Hi everyone;
I've got this question concerning absolute value, although I understand the concept of absolute value, I can't quite understand why option B is bigger than option A.
I would really appreciate some explanation on the following question:
I am trying to post it in Latex, but in case that the comparison is not properly viewed, here is how it goes:
Option A
(everything inside absolute value symbol, the two vertical lines), sqrt2 - 1
Option B
(everything inside absolute value symbol, the two vertical lines)
1/2 - 1

I am getting very confused with something that appears to be simple and basic enough, do I need to review some other concepts? arithmetic and/or number properties? if so can someone pin point me to some web based explanations.
Thanks
And cheers to everyone
You seem to be asking whether |sqrt(2) - 1| < |1/2 - 1|. (Note that the | character is on the same key as the \ character.)
The left side is about 0.414. The right side is exactly 0.5.

The only thing the absolute value function does is return the magnitude (distance from 0) of the expression inside the vertical bars. There's really nothing very mysterious here.
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,792
920
There was nothing at all "arrogant" about tic-tacs response.

He assumed you know, or could use a calculator to find that [itex]\sqrt{2}[/itex] is about 1.414 and so [itex]\sqrt{2}- 1[/itex] is about .414. Then [math]|\sqrt{2}-1|[/math] is about .414.

1/2- 1 is, of course, -1/2= -.5 so |1/2- 1|= .5 and .414< .5. That is all he was saying and is a complete answer to your question.
 

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