piclist 2001\06\03\003649a >
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : James Newton. Admin 3 email (remove spam text)

"...by an infinitely small (but non-zero) amount...."

To paraphrase a popular space opera "Never underestimate the power of the
infinity." Infinity is a mind-numbingly large (or small) thing. A totally
incomprehensible value. Anyone who can actually understand it's magnitude,
would be insane. It is one of the many things in life that one must not try
to completely investigate but rather to, at some point, simply accept.

I always enjoyed a story that a teacher of mine told about a class of
juvenal delinquents that he once enjoyed and tried to inspire. He told them
that they could not walk from one end of a class room to the other. He felt
that in a class of "normal" kids, the students would have sat, smiling,
waiting for the teacher to go on, but in this class one of the kids popped
up, walked to the back wall, then to the front then said "shows what you
know, sucker" and sat down to the applause of his classmates. The teacher
then went on to explain that in order to walk from one end to the other, you
first must walk half way. But then to complete the task, you have to walk
half the remaining distance, and so on (here it comes) * infinitely * so
that you never actually reach the other end, because you always have half
way left to go. The kids thought about it and then one said, "that's bull
shit teach, I know can still walk all the way" and  another said "no man,
he's right, you can get that close, but you actually never get there!" And
before the shanks came out, the teacher said "Does it really make a
difference? Can you get close enough that it doesn't matter? If you just
keep walking WILL YOU STILL BREAK YOUR NOSE!!!???" and the kids were willing
to accept that it probably isn't a good thing to understand that you can't
actually get from one wall to another.

Anyway, the point is, if you can believe that you can walk from one end of a
room to the other, then you can believe that infinitely small IS zero and
that 4.999 repeating is 5 and that you need to round even to avoid bias.

In fact, this is the main difference between engineers and technicians. The
difference between things making sense and things working.