One way to think about this is that we represent numbers in different ways. For example, 1 can be 1.0, or a single hash mark, or a dot, or 1/1, or 10/10. All of them point to some platonic ideal world version of the concept of the number 1.
What we have here is two different representations of the same number that are in a similar representation. 1 and 0.999… both point to the same concept.
It’s a correct proof.
One way to think about this is that we represent numbers in different ways. For example, 1 can be 1.0, or a single hash mark, or a dot, or 1/1, or 10/10. All of them point to some platonic ideal world version of the concept of the number 1.
What we have here is two different representations of the same number that are in a similar representation. 1 and 0.999… both point to the same concept.