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The meaning of the notation 0.999... is the least point on the number line lying to the right of all of the numbers 0.9, 0.99, 0.999, etc. ... every number larger ...
1 troy ounce of four nines fine gold (999.9) Nines are an informal logarithmic notation for proportions very near to one or, equivalently, percentages very near 100%. Put simply, "nines" are the number of consecutive nines in a percentage such as 99% (two nines) [1] or a decimal fraction such as 0.999 (three nines).
The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]
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.
The real numbers can be defined synthetically as an ordered field satisfying some version of the completeness axiom.Different versions of this axiom are all equivalent in the sense that any ordered field that satisfies one form of completeness satisfies all of them, apart from Cauchy completeness and nested intervals theorem, which are strictly weaker in that there are non Archimedean fields ...
The string "0.000...1" is not a meaningful real decimal because, although a decimal representation of a real number has a potentially infinite number of decimal places, each of the decimal places is a finite distance from the decimal point; the meaning of digit d being k places past the decimal point is that the digit contributes d · 10-k ...
Q: You guys talk a lot about real analysis, limits, and calculus; shouldn't this just be about arithmetic? A: Unfortunately, in order to formally prove many qualities of numbers, one often has to resort to higher mathematics: real analysis in the case of real numbers, number theory in the case of integers, and so forth.
(Excuse my English) Hello. In my opinion, any references to the real numbers should be deleted from this article, because . 0.999... is a notation for the limit of a sequence of n