In the spirit of Vi Hart (see www.youtube.com/watch?v=TINfzxSnnIE and www.youtube.com/watch?v=wsOXvQn3JuE) let me offer three reasons why 0.999... DOES NOT EXIST. 1. Any number that is as controversial as 0.999... must have something inherently logically inconsistent about it. 2. Mathematicians will tell you that 0.999... means you keep adding forever. But if you keep at it forever, you'll never arrive at an answer, so the answer doesn't exist. 3. A number that starts with 0.9 is at least as big as 0.9 but not as big as 1.0 (think about what it means when you divide 1 by 3 and get the first digit in the quotient to be 3). Likewise, a number that starts with 0.99 is at least as big as 0.99 but not as big as 1.00. Etc. So 0.999... means a number that's at least as big as all the numbers 0.9, 0.99, etc. but not as big as any of the numbers 1.0, 1.00, etc. And mathematicians themselves admit that there's no such number! Jim Propp P.S. Smileys will be omitted but are to be understood to be present throughout this post. If you don't know the standard theory of the real numbers, you may misunderstand Vi Hart's mischief, and mine. If you DO know the standard theory, please be assured that I know it too! On Mon, Jan 28, 2013 at 7:16 AM, Eric Angelini <Eric.Angelini@kntv.be>wrote:
Hello Math-Fun, à propos the table "Repeating decimal expansion", here: http://thestarman.pcministry.com/math/rec/RepeatDec.htm
... I read that: 1/2 = 0.5 1/4 = 0.25 1/5 = 0.2
... but is this equivalent to: 1/2 = 0.499999999999999999999999999999... 1/4 = 0.249999999999999999999999999999... 1/5 = 0.199999999999999999999999999999...
And what about: 1/3 = 0.6666666666666666666666666666666... ... re-written as: 1/3 = 0.6599999999999999999999999999999... 1/3 = 0.6666659999999999999999999999999... 1/3 = 0.6666666666666666666666599999999...
I'm confused. Best, É.
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