He doesn't call on me anymore.

And

**now**, it's time for...

*Duck's Classroom Corner*

-with Professor Duck

Today, Duck will prove to you that 2

^{n}= 0, where n is any natural number.

First off, we know that 2

^{n}- 1 = 2

^{0}+ 2

^{1}+ 2

^{2}+ 2

^{3}+ ... + 2

^{n - 2}+ 2

^{n - 1}

In binary, the i

^{th}bit of a bitstring, starting at 0 and from the rightmost bit, is equal to 2

^{i}. Therefore, the righthand side of the equation becomes the bitstring 1111...11

But! In binary, the most significant (or left-most) bit is known as the

*sign bit*, meaning that it indicates whether the number is positive or negative. Let's show our bitstring again, with the most significant bit highlighted:

1111...11

Since the most significant bit is 1, this number is clearly negative. But negative what? To negate a two's-complement binary number, you invert every bit and add 1 to the result. Let's investigate further:

1111...11 <= What we started with

0000...00 <= After inverting each bit

0000...01 <= After adding 1

So we see that the negative of 1111...11 is just 1; therefore, 1111...11 = -1.

But recalling our previous equality, we know that 2

^{n}- 1 = 1111...11, and by the transitive property of equality, we know therefore that 2

^{n}- 1 = -1.

After adding one to both sides, we arrive at our final result:

2

^{n}= 0

Next class, Duck proves that the total number of dead in the Holocaust was also 0... or, as Duck might say, 2

^{n}.

Debora, you might want to stop reading at this point.

Y'all should visit this site.

Where else could you find a woman telling you that John Kerry eats fetal stems cells, will kill every unborn child in the world, will kill every newborn male of the Hebrews, and will elect activist judges like Saddam Hussein to the Supreme Court?

*That's*something the liberal media won't report!

Nor do they seem to be making widely known the massive ignorance (or possibly denial) of Bush's constituency.

## 2 comments:

Nice bit of arithmetic hooey hiding in the guise of infinite series, but your first equality isn't. Jeez.

You're not very bright, are you?

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