At this time in history negative numbers were still being dismissed by European
ID: 2984908 • Letter: A
Question
At this time in history negative numbers were still being dismissed by European mathematicians. (Why do you think that the Greeks would be particularly troubled by negative numbers?) You want your students to have a better understanding of the uses of integers than early Greek mathematician so you have asked them to explain why the product of two negatives is positive. One of your students submitted the following explanation.
(-1)(-1) = (-1)(-1) + (0)(1)
= (-1)(-1) + (-1 + 1)(1)
= (-1)(-1) + (-1)(1) + (1)(1)
= (-1)(-1 + 1) + (1)(1)
= (-1)(0) + (1)(1)
= (1)(1)
= 1
Do you find the explanation reasonable? If you do, provide reasons for each statement in the explanation. If you do not, explain why it is unreasonable. Did the student use the equal signs in an appropriate way? OR
Explain why the derivative of the area formula for a circle equals the circumference formula, and the derivative of the volume formula for a sphere equals the surface area formula. (The point of this problem is not to demonstrate your ability to take a derivative but to explain why these relationships are reasonable.)
Explanation / Answer
yes, the explanation is reasonable. In a set of integer Group G,let a be an element then, a*1 = a a*0 = 0 0 can be written as a-a according to the distributive law, (a+b)*c = a*c + b*c ; since all the laws are used properly in the proof explanation is reasonable.
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