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Re: Please remind me why 3^2 = 9
Posted:
Nov 18, 2012 9:54 AM


The statement below is not true if one is interpreting 3^2 as the square of 3.
73^2 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: 73^2 means 7+3^2 means 7+(1*3)^2.
Also I agree that "73^2 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.  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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