True or false? When \( n \) is a negative integer, \( n - n = 0 \). Justify your response.

This would be true. It is a trick question if you didn't pay attention to the negative. Just try substituting the n s for negative integers. For example: -4--4. The negatives rule each other out and then -4+4=0.

Answered by pinkster104 | 2024-06-10

The statement that n - n equals zero is true for any integer n, including negative integers, due to the additive inverse property.

The statement provided is true. Regardless of whether n is a positive or negative integer, the result of n subtracted by itself will always be zero. The property in question here is the additive inverse property, which states that for every integer n, there exists an additive inverse, which is -n, such that n + (-n) = 0. When we replace the additive inverse with the same number, the equation becomes n - n = 0. This property holds true for any integer whether it is positive, negative, or even zero.

Answered by ToddBoyce | 2024-06-24

The statement n − n = 0 is true for any integer, including negative integers. Subtracting a number from itself always results in zero. Therefore, whether n is a negative integer or not, the result will always be zero.
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Answered by pinkster104 | 2024-09-03