Re: Re: 0.999...
|Originally posted by Looney4Clooney |
that would not be a real number if the 9 extends to infinity.
Actually, it would be -- one casual definition of a "real number" is just that it is any number that can be represented by an infinite decimal (even if, as in the case of integers, that infinite decimal would just be something like 1.000000...).
|Originally posted by Joss Weatherby |
Essentially it can't be a number because it is constantly changing, its always going to be more or less than itself, never equal, and not any other number.
The mistake here is in thinking of a number as being created by a "process" such as adding numbers one by one after the decimal point. A number isn't an algorithm, it's just an abstract mathematical object that is always the same thing independent of representations or means of calculation.