I was thinking it was the limit of something... but it's definitely like Zeno's paradox of motion (that you mention above). Though I studied that in philosophy--not math--class.

third line asserts additional information from nowhere. if x(x-1)= 0 and x already was given as 0, then x-1 must equal -1.

 

Yeah, the dichotomy paradox is the same as the paradox of motion.

Explanation for those not versed in Zeno:

Imagine that you are playing American football. You have received the kickoff while standing precisely on the goal line, and you wish to run the ball across the field for a touchdown, a distance of precisely 100 yards. (We will assume that you are an infinately good player, and can easily avoid the defense while traveling in a straight line towards their goal.)

The paradox is that in order to travel any distance, you must first travel half that distance.

So you run half the distance, and you are now on the 50 yard line. From that point, you run half the remaining distance, and you are now on the 25 yard line. From there, you run half the remaining distance and find yourself at the 12.5 yard line.

You will continue in this manner, travelling smaller and smaller distances each time (eg: from the one-eighth-inch line to the one-sixteenth-inch line) however you will never actually reach the goal itself. And as you stand there pondering this, you will be tackled.

Ergo, philosophers are shitty football players.



I know, it's just kind of funny in the same way as the proof that women are evil because time is money.

 

here is the cruelest nerd joke and it's dedicated to Joe and his sig:

I've actually personally seen the MS3 schematics with my own eyes.

 

That's just mean.

 

Keep 'em coming!

I didn't know that ME's studied control theory.

 

absolutely, it's a required course. we build all sorts of neat upside down pendulum things.