Using calculus (an infinite series to be more exact), we know that .999 repeating can actually be written as The sum from 0 to infinity of(.9(.1^n)), which is a geometric series of the form a=.9, r=.1. (Meaning that it follows the form a+ar1+ar2+ar3... etc.) Using the geometric series convergence rule, we know that any geometric series converges to a/(1-r). So, the series converges to .9/(1-.1), or .9/.9, which obviously equals 1. This is an infallible proof, using one of the highest levels of math (differential Calculus), that cannot be disproved, and although it conflicts with my sense of logic, .999 repeating equals 1. You can't argue with it in any way, shape, or form. 1 equals .999 repeating and there's not really anything any of us can do about it, unless you want to get mad at Euler and Isaac Newton.
Common sense... 1/3 = .33 repeated 2/3 = .66 repeated 3/3 = .99 = 1 Mathematic loophole. No big deal. Seems to me like you just learned this...
This has been around for a long time, however if you ask a math teacher if .999=1, they will send you back to the first grade. Just look at it, don't be a smart ass.
in all my HS math teachers have had bachelors degrees in math and in one case a PHD. my college profs have all had masters or higher
This. Also, .99999999999999999999999999999999999999999999 = .99999999999999999999999999999999999999999999
agreed .99999999999999999999999999999999999999999999 =.99999999999999999999999999999999999999999999 != 1 but .9999... = 1 think of it this way. You have a piece of paper. It's 1 square mile. You start curring it into pieces. one piece is 9/10ths of the area. The next piece is 9/10s of the remaining area. And the next piece 9/10s of the ramaining area. if you add up the pieces you cut you'll get .9+.09+.009+.009 and so on until you have .999 recurring. but just because you cut the paper doesn't mean you have any less paper.