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The Archimedean property: any point x before the finish line lies between two of the points P n (inclusive).. It is possible to prove the equation 0.999... = 1 using just the mathematical tools of comparison and addition of (finite) decimal numbers, without any reference to more advanced topics such as series and limits.
This page is for mathematical arguments concerning 0.999... Previous discussions have been archived from the main talk page, which is now reserved for editorial discussions.
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The notation 0.999..., as said, denotes a "repeating decimal", and is not prepared to be amended to 0.999...9, because this latter notation totally loses the meaning of a "repeating decimal". It denotes a decimal with an unspecified, but finite number of 9 s right to the decimal point.
You have to be sure though when claiming that it is one, to point out that it is really (1 - .0000...1) While the difference between .999... and 1 is infinitely nothing, it cannot be dismissed because it is everywhere..000...1 is the first thing there is greater than zero, and it's between every change between every two numbers all the way up to one.
A: If you have a number like 0.999...9, it is not the last number in the sequence (0.9, 0.99, ...); you can always create 0.999...99, which is a higher number. The limit 0.999 … = lim n → ∞ 0. 99 … 9 ⏟ n {\displaystyle 0.999\ldots =\lim _{n\to \infty }0.\underbrace {99\ldots 9} _{n}} is not defined as the highest number in the ...
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...
More or less by definition, 1/3 is the number which, when multiplied by 3, gives 1. (In general, a/b is the number which, when multiplied by b, gives a.) This does not depend on rounding. Yours, Huon 14:13, 18 May 2006 (UTC) IM SORRY TO SAY THAT WHEN YOU MUTIPLY 0.3 * 3 YOU GET 0.9 A.R.B You needn't be sorry for that; I agree.