Kenjuudo wrote:
Both of you fail to see that the value 0 is not a physical value, but a mental approximation, or thought experiment if you will, about the concept of nothing (even if "nothing" doesn't exist). It's a mentally constructed model. Just like the math generally isn't trying to describe nature exactly which is impossible anyway, but is a tool to describe nature as closely as possible. In nature, there are actually no numbers at all. No zeros, no ones, no twos. They are just intellectual tools, or attributes, we apply to nature to create order in the apparent chaos.
There are many possible interpretations of "0", but approximation of anything is not a good one. Some measured quantity may be approximately zero, but zero is not approximately anything; it is exactly 0. A better way to put it is that "0" is a thing which satisfies certain formal manipulations. In any
>>>ring,<<< we can conceive of 0 as that element of the ring satisfying a+0=a.
Quote:
Removing "to the power of 2" in the 6th step causes the generation of an imaginary number on the left side.
(4 - 9/2) is negative and is equal to -0.5. -0.5^2 = -0.25 (not 0.25 as the image says). Finally, the square root of -0.25 is 0 + 0.5 i.
Thus the proof is invalid.
Right, somewhat more precisely, however, we observe that it is in general fallacious to say that x^2=y^2 => x=y. Obviously, this doesn't work because (-1)^2=1^2, yet -1 != 1. The problem is that people tend to think of operations as necessarily invertible, which they aren't necessarily. Because the function x^2 is not one to one, it is not invertible over its domain, and hence we can't undo it to find a unique solution to the equation.
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* here for the nachos.
27 Jun 2009, 11:08 am
