What are the cases you refer to ?astrololo said:Homework Statement
I must prove that the mean of one number and its absolute value is superior or equal to 0 but inferior or equal to the absolute value of the number
Homework Equations
I must prove this by the method of case.
The Attempt at a Solution
I know that the first case is : x>=0 and the second x<0
But after that, I have no idea on how to do this...
You mean you don't understand what the proof by case is ? I mean that to arrive to my result, I must begin x>=0 and the second case is x<0. After, I imagine there is some sort of addition that I Must do to obtain my final result.SammyS said:What are the cases you refer to ?
Are you still here ? I think that I must do this : x<0 then absolute(x)=-xSammyS said:What are the cases you refer to ?
I misread your post.astrololo said:You mean you don't understand what the proof by case is ? I mean that to arrive to my result, I must begin x>=0 and the second case is x<0. After, I imagine there is some sort of addition that I Must do to obtain my final result.
Then this means |x|=xSammyS said:I misread your post.
Case 1: x ≥ 0
If x ≥ 0, what is |x| ?
Yes. That's the way to start each part.astrololo said:Are you still here ? I think that I must do this : x<0 then absolute(x)=-x
and x>=0 then absolute(x)=x
Yeah, I was able to understand this. Here is what I did after :SammyS said:Yes. That's the way to start each part.
Yes.astrololo said:Yeah, I was able to understand this. Here is what I did after :
|x|=x add x on each side
|x|+x=2x
divide by 2
(|x|+x)/2=x
Case 2 :
|x|=-x
|x|+x=x-x
|x|+x=0
Multiply by 1/2 by each side.
(|x|+x)/2=0
Is this correct ?
Ok, I guess that I must use my x<=0 inequality and replace the x.SammyS said:Yes.
astrololo said:Ok, I guess that I must use my x<=0 inequality and replace the x.
(|x|+x)/2<=0
The formula for finding the mean of a number and its absolute value is (x + |x|) / 2, where x is the given number.
The mean of a number and its absolute value represents the average distance of the number from zero. It takes into account both positive and negative values.
No, the mean of a number and its absolute value will always be a positive value. This is because the absolute value of a number is always positive, and when added to the number, it increases the overall value.
The mean of a number and its absolute value will remain the same regardless of whether the number is positive or negative. This is because when a negative number is added to its absolute value, the result is always positive.
In addition to the mean, the median and mode can also be used as measures of central tendency for a number and its absolute value. However, the mean is the most commonly used measure in this case.