Anonymous
10/19/2025, 2:36:27 AM
No.16820411
There are no nonzero infinitesimals in arithmetic. By asserting a zero followed by infinitely many nines you are constructing a specific hyperreal number however the notation 0.999... does NOT refer to that number. You are constructing a number that isn't allowed by the rules of arithmetic, simple as that.
You are invoking a very different type of infinity here, by saying the "last" 9 is after an unending sequence of 9s you are implicitly creating a number that you defined to be larger than any finite number and then ordering your 9 at that spot and that number is in fact the smallest ordinal number. By bringing transfinite numbers into arithmetic you are playing fast and loose with the rules and your expression is invalid because you're trying to evaluate two objects of different classes. What is the char 'c' + 17 equal to? Nothing, you can only parse it by casting the char using some arbitrary pattern.
When working with infinities you must take care to define exactly what you mean by "infinite" and if it applies to your problem or is it strictly excluded by definition. When you evaluate the "infinite" amount of 9s in 0.999... as a limit you do end up with a 1.
You are invoking a very different type of infinity here, by saying the "last" 9 is after an unending sequence of 9s you are implicitly creating a number that you defined to be larger than any finite number and then ordering your 9 at that spot and that number is in fact the smallest ordinal number. By bringing transfinite numbers into arithmetic you are playing fast and loose with the rules and your expression is invalid because you're trying to evaluate two objects of different classes. What is the char 'c' + 17 equal to? Nothing, you can only parse it by casting the char using some arbitrary pattern.
When working with infinities you must take care to define exactly what you mean by "infinite" and if it applies to your problem or is it strictly excluded by definition. When you evaluate the "infinite" amount of 9s in 0.999... as a limit you do end up with a 1.