In mathematics, 0.999... (also written as 0.9, 0.. 9, or 0. (9)) is a repeating decimal that is an alternative way of writing the number 1. Following the standard rules for representing numbers …

We can think of 0.999... as being equal to: = 0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9×0.10 + 0.9×0.11 + 0.9×0.12 + ... This is an Infinite Geometric Series where a = 0.9 and r = 0.1 with …

Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of nines: 0.99999… It may come as a surprise when you first learn the fact that …

0.999... is a repeating decimal, which means the digit "9" is repeated forever. It is different from 0.999, which only has three 9s. 0.999... can also be written as or . It is hard for many people to …

Why some people say it's false: It's less than one, since it starts with 0.99 instead of 1.00. So it cannot be equal to 1. Intuitive explanation: Visualize a number line. If two real numbers on the …

What is 0.999… equal to? The infinite repeating decimal 0.999… is equal to the whole number 1. This is very different from the value of, say, 0.999, which is equal to \frac {999} {1000} …

There are many proofs that the repeating decimal 0.999... is equivalent to the number one, some more rigorous than others. Also with counter-proofs. The notion that 0.999... represents an …

2023年9月18日 · As a matter of precision, however far you take this pattern, the difference between 1 and a bunch of 9s will be a bunch of 0s ending with a 1. As we do this thousands …

2011年5月11日 · What we see here is that 0.9999… is closer to 1 than any real number (since we showed that 1-0.9999… must be smaller than every positive number). This is intuitive given …

2014年6月2日 · When you have an infinitely decreasing number does it ever hit a point where it is indistinguishable from the number it’s approaching? Does 0.999999999…, for instance, ever …