Show the conhecture is false by finding a counterexample...
1. The differnece of the absolute value of two numbers is positive meaning
/a/ - /b/ > 0
I do not get that.... =/
HELP.
If absolute value of a is greater than the absolute value of b, then the difference has to be positive, greater than zero.
example: a= -7
b=4
abs a= 7
abs b= 4
abs a - abs b=3, or it is greater than zero.
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To show that the conjecture is false, you can find a counterexample. In this case, a counterexample would be two numbers where the difference of their absolute values is not greater than zero.
Let's take the numbers -7 and 4 as an example. The absolute value of -7 is 7, and the absolute value of 4 is 4. If we subtract the absolute value of 4 from the absolute value of -7, we get 7 - 4 = 3. This difference is positive and greater than zero, which supports the conjecture.
However, if we want to find a counterexample, we need to find two numbers where the difference of their absolute values is not greater than zero. Let's try a = -4 and b = -7.
The absolute value of -4 is 4, and the absolute value of -7 is 7. If we subtract the absolute value of -7 from the absolute value of -4, we get 4 - 7 = -3. This difference is negative (-3), which means it is not greater than zero.
Therefore, the counterexample (-4, -7) shows that the conjecture is false. The difference of the absolute value of these two numbers is not greater than zero.
a= -7
b=4