- #1
cmurphy
- 30
- 0
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?
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.
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.
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.
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.
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.