>>11544363>Generally we have terminating conditions by the calculations required to achieve said number. By using (...) you are overriding those termination conditions.I can calculate 1/3 = 0.333... in only three steps. It's easy to get an infinitely repeating decimal with a finite calculation.
>(...) implies it is a sequenceNo, it implies the decimal repeats without end.
All real numbers can be represented by sequences of numbers that converge towards a certain value. This is one way of constructing the real numbers. The decimal truncations of 0.999... and 1.000... are sequences that converge to the same number, 1. Therefore 0.999... and 1 are the same number.
Another way to construct real numbers is to divide the number line into two sets A and B such that every element of A is less than every element of B, and A has no greatest element. Since every number less than 0.999... is also less than 1, this means 0.999... and 1 are the same number.
