Help mee please ~ อิ้งอิ้ง
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1
One Equals Zero
Explanation
The error occurred when the factor x - 1 was canceled. Because x = 1, x - 1, and it is obviously incorrect to deduce from the statement 0 * (x + 1) = 0 that x + 1 = 1. Canceling factors without considering the possibility that a factor could be Zero is a common error.
_________
Comment
Cancellation is division of both sides of an equation by the same nonzero factor. This activity serves as a warning against dividing both sides of an equation by a factor that could be zero. The purpose of this activity is to accentuate the danger of forgetting that cancellation is defined as dividing both sides by a nonzero factor.
When students have completed this activity, they may consider the formal reason for ruling out division by zero of any nonzero number and for ruling out division by zero of zero, which are very different from each other. The reason in both cases is that division by zero cannot be well defined. Division of a nonzero number by zero is undefined because there is no solution to the equation a * 0 = b if b is not zero. If b s zero, there are infinitely many solutions to a * 0 = b and division by zero cannot be uniquely difined, which is the same as saying that it is not well defined.
_________
See Also
See also Activities 2, 3, 7, 15, and 26.
1
One Equals Zero
Explanation
The error occurred when the factor x - 1 was canceled. Because x = 1, x - 1, and it is obviously incorrect to deduce from the statement 0 * (x + 1) = 0 that x + 1 = 1. Canceling factors without considering the possibility that a factor could be Zero is a common error.
_________
Comment
Cancellation is division of both sides of an equation by the same nonzero factor. This activity serves as a warning against dividing both sides of an equation by a factor that could be zero. The purpose of this activity is to accentuate the danger of forgetting that cancellation is defined as dividing both sides by a nonzero factor.
When students have completed this activity, they may consider the formal reason for ruling out division by zero of any nonzero number and for ruling out division by zero of zero, which are very different from each other. The reason in both cases is that division by zero cannot be well defined. Division of a nonzero number by zero is undefined because there is no solution to the equation a * 0 = b if b is not zero. If b s zero, there are infinitely many solutions to a * 0 = b and division by zero cannot be uniquely difined, which is the same as saying that it is not well defined.
_________
See Also
See also Activities 2, 3, 7, 15, and 26.
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