Search results
Results from the WOW.Com Content Network
So, it does not make sense to identify 0.999... with any number smaller than 1. Meanwhile, every number larger than 1 will be larger than any decimal of the form 0.999...9 for any finite number of nines. Therefore, 0.999... cannot be identified with any number larger than 1, either.
Indeed, that difference is the sequence (0.1, 0.01, 0.001, ...). This sequence does indeed converge to 0 (straightforward exercise for the reader), which means that the two sequences are in the same equivalence class, which means that "0.999..." and "1" represent the same real number, by definition. Short and sweet.
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).
This object would represent a different number than the topic of this article, and this notation has no use in applied mathematics. Moreover, it does not change the fact that 0.999... = 1 in the real number system. The fact that 0.999... = 1 is not a "problem" with the real number system and is not something that other number systems "fix".
OK... I learned about 0.(9) being the same as 1 in high school too... But now I have this question. 1 = 0.99999... right? 2 = 1.99999... every ok so far. does this ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
1 is a rational number, .999...... is not a rational number. By definition an irrational number is a number which cannot be expressed as a fraction m/n, where m and n ...
It is perfectly true that 0.999...999 with any natural number of nines denotes a real number that is less than 1. But "0.999..." is shorthand for saying that there are an infinite number of nines. Infinity is not a natural number.