Proving the definition of abs. value

Thread starter cmurphy
Start date Jan 23, 2005
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In summary, the definition of absolute value is the distance of a number from 0 on a number line, always resulting in a positive value. To prove this definition, one can use the properties of absolute value, such as its positivity and the fact that the absolute value of a negative number is its positive counterpart. This concept is useful in real-life situations, such as calculating distances and solving equations. A common misconception is that absolute value always results in a positive number, but this is only true for negative numbers.

Jan 23, 2005

cmurphy

I need to show that the absolute value of x = max {x, -x}. Of course I know this is true, but I must show this. How would I go about doing such a thing?

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Jan 23, 2005

arildno

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The absolute value is always positive, right?
Use that fact.

Jan 23, 2005

dextercioby

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BTW,a definition cannot be proved...

Lemmas,theorems,properties,propositions,corolaries,but not definitions...

Daniel.

1. What is the definition of absolute value?

The absolute value of a number is its distance from 0 on a number line. It is always a positive value, regardless of the sign of the original number.

2. How do you prove the definition of absolute value?

To prove the definition of absolute value, you can use the properties of absolute value, such as the fact that it is always positive and that the absolute value of a negative number is the same as its positive counterpart.

3. Can you give an example of proving the definition of absolute value?

Sure, for example, to prove that the absolute value of -5 is 5, we can use the fact that the absolute value of a negative number is its positive counterpart. So, the absolute value of -5 is the same as the absolute value of 5, which is 5.

4. How is the definition of absolute value useful in real life?

The definition of absolute value is useful in many real-life situations, such as calculating distances, determining the magnitude of a force, or finding the error in a measurement. It is also used in solving equations and inequalities.

5. Are there any common misconceptions about the definition of absolute value?

Yes, a common misconception is that absolute value always results in a positive number. However, the absolute value of 0 is 0, and the absolute value of a positive number is the same number. It is only negative numbers that result in a positive value when taking the absolute value.