The missing o.ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo1 !! This reminds me on correcting Newtonian physics. https://www.youtube.com/watch?v=IM630Z8lho8"]https://www.youtube.com/watch?v=IM630Z8lho8
yeah, but i can't think of any other situation in math where "for all reasonable intents and purposes" is considered a satisfactory explanation.
i did think of that one, but then aren't they still working on calculating that down to the several thousandth decimal point or something?
Whoa! Just looked it up. Pi has been calculated into the 10s of trillions of a decimal point. That is nucking futs!
Oh yes, I discovered this in high school algebra and it messed with me for years until a friend who took a lot of differential calculus explained it to me. Basically it has to do with a concept called the limit. Let's say that x = 0.999999... and we want the ratio (fraction) equivalent of x. Since we've got as many nines as we want, we can then say that 10x = 9.999999... (to move the decimal point over by one place), which is really just like saying 10x = 9 + x since we still have an infinite number of nines. Now we can just subtract x from each side and get 9x = 9, and then divide each side by 9 and get...surprise!...x = 1. OK, so WTF is going on here?? Let's say we want to build 0.999999... in the other direction. Well, first we start with 0.9 whch is just plain old ordinary 0.9...but we have to add the next nine. We do that by adding 0.09 (since 0.9 + 0.09 = 0.99). But we're not done yet! We still have an infinite number of nines to go, so we need to turn 0.99 into 0.999. We do that, of course, by adding 0.009. It goes like this: 0.9 + 0.09 = 0.99 0.99 + 0.009 = 0.999 0.999 + 0.0009 = 0.9999 0.9999 + 0.00009 = 0.99999 To add each nine, we have to keep tacking zeros on at each step. The steps always get smaller, but there's an infinite number of them, so by the time the step size reaches zero (an infinite number of steps later), the sum would already be at 1. The one is just the limit, which is basically a way of saying "If you could do this step forever, this is where you'd be." That's an oversimplification, but it works for this purpose. Since our decimal number system is not really designed to handle infinite mindfucks like this, it leads to the glitch that makes "0.999999... = 1" a true statement even though our minds look at it and go "No! No! Those are not equal!"
