Hi guys,
never posted before because i'm afraid i'm not as technically proficient with FIRST robotics as a lot of you, but, if there's one thing i know, it's calculus.
.999~ (.999 recurring or repeating as its commonly known) does in fact equal one. The "Multiply by Ten" Proof is true, but difficult to grasp for the common mind, so suffice to say that this proves it once and for all: (granted someone already did mention this)
A infinite geometric series is a series of numbers where one begins with a set point (the First element) and finds the next point by multiplying the First element by some number X. Then, to find the next number in the sequence, you keep on taking the number you have and multiplying by X (X is called the common ratio, in fact). Odd as it may seem, such infinite series of numbers do in fact add up to definite finite real values. The sum of an infinite geometric series is A / (1 - R) where A is the First element of the series and R is the common ratio. In this case, The series is .9 + .09 + .009 + . 0009 ad infinitum. Thus, the First element "A" is clearly .9 and the Common Ratio "R" is clearly .1 , or One-Tenth. Now, consider: in this case, A / (1 - R) = .9 / (1 - .1) which equals .9/.9 which of course equals 1. Ta da! For those of you who don't believe this geometric series sum rule i am using, there are myriad other ways to show the fact, such as the calculus' Ratio test, etc.
Meanwhile, this is a fascinating discussion, and I enjoyed reading everyone's thoughts. Someone mentioned the idea of 0/0. There's a name for it, and I seem to forget exactly what the name is (the name does make sense once you hear it). Anyway it's not 0; 0/0 is equal to INF/INF or 1^INF or 0^0 or any other myriad devilish expressions : it simply does not exist. I think it might be called an infinite discontinuity but that's just a guess. anyhow, there's math for ya!
captain dan
team 1168
www.friarbot.com rocks my world too hard