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In Academian mathematics, negative and positive are kinda like opposites. But are they really equal opposites, in compliance with the Principle of Opposites?

The equations +1 × +1 = +1 and -1 × -1 = +1 suggest that they are, in fact, NOT equal opposites. The fact that Academians consider the square of a positive number and the square of a negative number to both be positive, suggests that they are biased towards positive. Clearly, this bias must be eliminated.

Let's do this by manipulating a graph. Here we see the function y = x2. The Academian convention of the square of a negative number being positive is represented in the graph by the fact that there are only positive "y" (+y) values in the negative "x" (-x) region of the graph.

Let's rectify this evil convention: Here we've flipped upside-down the portion of the graph located left of the y-axis. Within this new rectified graph, there are negative y (-y) values corresponding to the negative x (-x) values. It represents -1 × -1 = -1 — that initial biased equation, but with the bias now rectified.

So we've eliminated the bias, but there's a problem: This graph shows the derivative (gradient) of the rectified x2 function. The derivative of the initial x2 graph is a single straight line, but this new derivative has two separate lines that terminate at zero. This is a discontinuity that needs to be rectified. And here it is rectified — we add to it its reflection about the x-axis. So this derivative graph is now composed of two continuous straight lines.

Now, what impact does this have on the initial rectified x2 graph? The impact is that we've added its reflection about the x-axis. Academians would represent this graph as y = ±x2.

And, in fact, this final graph represents the principle of opposites — in that it's the same shape when flipped in the x-axis, and the same shape when flipped in the y-axis. So, it rightfully represents positive and negative as equal opposites.

Let's now think about square roots. According to Academia, the square root of +1 is ±1. So, by the principle of opposites, the square root of -1 should also be ±1.

But since Academians believe that negative squares don't exist, they have to introduce an imaginary number. They call it i and define it as i2 = -1.

Let's use Academian mathematics to perform a few manipulations on i. So now, as well as the initial i = sqrt(-1) ("sqrt" = "square root"), we have i = ±1 — as predicted! Academians, however, don't like this at all.

Consider this: if you can say x2 = 4 and convert that to x = sqrt(4), then there's no reason why you can't also take the definition i2 = -1, and convert it to i = sqrt(-1), right?

Academians say "Wrong!", and they try to get around it by imposing an arbitrary limit. When presented with i = sqrt(-1) — a direct consequence of the definition i2 = -1 — they say "You can't do that!". Why? "You just can't!". Well, surely we must demand that mathematics be consistent. If performing a standard mathematical manipulation causes the entire system to implode, then the system is flawed and must be fixed. It really is that simple.

Let's witness the mathematical system imploding as we perform one further manipulation: From i = sqrt(-1), we have now obtained the initial definition — i2 = -1! This confirms that contrary to the unfounded assertions of Academian pedants, it is in fact perfectly legal to go from i2 = -1 to i = sqrt(-1).

In conclusion, we have established that the equation -1 × -1 = +1, and the imaginary numbers, are both evil frauds invented by Academian pedants. From the graphs, we've established that +1 × +1 = ±1 and -1 × -1 = ±1; and we've established that sqrt(+1) = sqrt(-1) = ±1. So, whereas the erroneous Academian concepts have failed to comply with the Principle of Opposites, the concepts we've established have gloriously succeeded.

Time Cube debunks god lies. Evil people deny Time Cube. Educators are flat-out liars. Evil media hides Time Cube. -1 x -1=+1 is stupid and evil. Word worship equates to evil. Bible induces a barren Earth. Evil 1 day Bible kills children.
— Gene Ray, timecube.com    © Cubic Awareness Online, 2004-2007.Time Cube © Gene Ray, www.TimeCube.com     