1.) Suppose you have quantities A and B, and suppose they are equal. That is,Step 3 is where it goes wrong. If a^2=AB, and you subtract B^2 from both sides, you have

A = B

2.) Multiply both sides by A:

A^2 = AB

3.) Now subtract B^2 from both sides:

A^2-B^2 = AB-B^2

4.) Factor both sides:

(A+B)(A-B) = B(A-B)

5.) Divide both sides by the common factor (A-B):

A+B = B

6.) Now, remembering that A=B, we have

B+B=B, or 2B=B

7.) Divide both sides by B:

2=1

*zero*. A^2=AB, therefore B^2=AB, because (as stated at the beginning) A=B. AB-B^2=0.

Furthermore, though, is the fact that while you can add whatever you want to any equation as long as you do it on both sides, it doesn't always make

*sense*to do so. Okay, 2x+b=y, you can make that 2x+b+GOOBER=y+GOOBER if you like--but that doesn't add any information to the equation; it merely makes it easier (theoretically) to manipulate. In this case, it reduces both sides to zero, which is an identity (zero always equals zero). That's not a solution to the equation; that's just proving that both sides are equal, which we already knew.

If you really want to prove that 2=1, you need to get your algebraic manipulations right. But of course if you do the algebra right, you won't

*get*2=1. Getting a result of 2=1 is a sure sign that you figured wrong.

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(There are cases where an equation has a null solution set, so if you do all the figuring right and still get something like 2=1 the correct answer is {}, ie a null set.)

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The preceding was sponsored by my wife's algebra class!!!

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They did it once. They could do it again.

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There is some doubt about what happened at Kent State, at least in my mind. I recall seeing a report that someone had been shooting at the National Guard, or at least firing a gun in their general vicinity. But the point is valid: the soldiers, "only ones", had firearms there, and they shot unarmed people.

That's what leftists want, though. They want to be able to control you, and to stomp on your face, and they can only do it if citizens aren't allowed to own guns.

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Interesting thing about

__The Man In The High Castle__: I see Nazism presented as a

*collectivist*philosophy, exactly the way it was. There's a funeral scene, and that funeral--stripped of any religion whatsoever--instead becomes a paean to

*collective service*. The dead man's service to his society and the state is what's lionized; there's no discussion of an eternal reward because Nazism was atheist.

Not to put too fine a point on it, but collective service is a big virtue for socialists. It's one of the planks of Kwanzaa, the great socialist-and-fake-african holiday.

And so this series portrays Nazism as it actually was:

*a socialist political system*.

It's horrifying, all right, because there's widespread extermination of "defectives". The point is made that doctors are required by law to report patients who have incurable diseases; they're derided as "useless eaters" and euthanized at the earliest opportunity.

Overall it's an extremely well-done series; the world-building is flawless. Not much is said about what happened to the USSR and China, but at some point we see a map of the world with Japanese and Nazi territories blocked out, and there is a rather slim chunk of Asia which is neither.

Basic premise is that Germany won WW2 because they developed the atom bomb first; they nuked Washington, D.C. in 1947 and the rest was just a mopping-up exercise. Nazi Germany with the Bomb would have walked all over the USSR, and because the rival socialisms hated each other--and because Germany and Russia are very, very old enemies--the USSR would have been flattened. And China didn't turn communist until 1950; with Japan running half of China, that simply would not be allowed. So there's no

*communism*in the world; just National Socialism.

...and we've got two episodes left of it. *sigh*

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Japanese guy doesn't care about being called "racist".

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WTF

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Well, it's Monday; what else can you say about it?