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Re: Please remind me why -3^2 = -9
Posted:
Nov 18, 2012 9:54 AM
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The statement below is not true if one is interpreting -3^2 as the square of -3.
7-3^2 means 7+-3^2 means 7+-1*3^2
To be true, the second part of that previous statement assumes that -3^2 means -(3^2), but that is assuming what we are trying to demonstrate from other principles. You cannot prove something by assuming it is true.
If one is interpreting -3^2 as the square of -3, a true statement would be:
7-3^2 means 7+-3^2 means 7+(-1*3)^2.
Also I agree that "7-3^2 means 7+-3^2" because the definition of a - b is a + (-b).
But -3 does not mean -1(3). They may be equivalent, and this equivalence may be useful to use, but -3 "means" the value which when added to 3, gives zero.
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I, and others, am not saying that -3^2 is interpreted as -9 is false, but only that it is totally an arbitrary interpretation, not logically deduced from our common axioms and definitions.
And I don't argue that there should be one correct interpretation, and that -9 is correct.
But I posed the original question because so many students get it wrong, even after a reasonable amount of stress on it, that it is clearly not an intuitive interpretation and really should not, therefore, be used in the first place.
Phil
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