|-2| = 2Please, explain the definition of absolute value as defined in the book.
"The absolute value of a real number a, denoted by the symbol |a|, is defined by |a| = a is a is >or= 0 and |a| = -a if a < 0."
Can you provide an example when we get -a?
|-2| = 2
Please, explain the definition of absolute value as defined in the book.
"The absolute value of a real number a, denoted by the symbol |a|, is defined by |a| = a is a is >or= 0 and |a| = -a if a < 0."
Can you provide an example when we get -a?
Did you think through it?No. Khan, provide an example in terms of - a.
Did you think through it?
It seems that you are posting super-elementary thoughts??!!
The problem here is that you have been given a definition in terms of a variable. The only pertinent examples will be numeric ones (otherwise you are just substituting one variable for another).So, give me a super-elementary answer, Mr. Khan.
|-2| = 2
Here is his example in terms of -a, as well as can be done, I think:No. Khan, provide an example in terms of - a.
Here is his example in terms of -a, as well as can be done, I think:
Suppose a = -2. Then
|a| = |-2| = 2, and-a = -(-2) = 2.So |a| = -a.
If that isn't clear, perhaps you can elaborate on your own thoughts about the definition. It's very common for students at first to be confused about negative numbers vs. negatives of numbers, as in "If a is negative, then -a is positive."
Here is his example in terms of -a, as well as can be done, I think:
Suppose a = -2. Then
|a| = |-2| = 2, and-a = -(-2) = 2.So |a| = -a.
If that isn't clear, perhaps you can elaborate on your own thoughts about the definition. It's very common for students at first to be confused about negative numbers vs. negatives of numbers, as in "If a is negative, then -a is positive."
[MATH]-\ |- 7| = -\ (\sqrt{(-\ 7)^2}) = -\ (\sqrt{49}) = -\ (7) = - 7.[/MATH]What about -|-7|?
- | -7 | = -7
[MATH]-\ |- 7| = -\ (\sqrt{(-\ 7)^2}) = -\ (\sqrt{49}) = -\ (7) = - 7.[/MATH]
In fact, by the definition, you can prove that
[MATH]-\ |a| \le 0.[/MATH]
|-2| = - (-2)Please, explain the definition of absolute value as defined in the book.
"The absolute value of a real number a, denoted by the symbol |a|, is defined by |a| = a is a is >or= 0 and |a| = -a if a < 0."
Can you provide an example when we get -a?
|-2| = - (-2)
There is your example. Just note that -(-2)=2
Correct - what is the point of contention/confusion?Yes but - |-2| = -( 2) = - 2.
Correct - what is the point of contention/confusion?
Yes but - |-2| = -( 2) = - 2.
What is the meaning of the "but"? Are you implying you see a contradiction with what had been said?Correct - what is the point of contention/confusion?
What is the meaning of the "but"? Are you implying you see a contradiction with what had been said?