> We can repeat this process for an infinite amount of time and still not have an infinite number of nines.
Isn't this somewhat ill-defined? You may have a finite number of 9s at any one point when adding more 9s, but there is no point "at infinity" where you can stop and look at how many 9s you've added because by definition there are still more 9s to add.
It's like trying to prove infinity is impossible:
> Assume that we have a finite number. Add 1 to that number. The result is not infinite. Add another 1. The result is still not infinite. We can repeat this process for an infinite amount of time and the number is still not infinity.
Sure, individual numbers "on the way" to infinity are not infinite, but that doesn't necessarily disprove the existence of infinity.
Isn't this somewhat ill-defined? You may have a finite number of 9s at any one point when adding more 9s, but there is no point "at infinity" where you can stop and look at how many 9s you've added because by definition there are still more 9s to add.
It's like trying to prove infinity is impossible:
> Assume that we have a finite number. Add 1 to that number. The result is not infinite. Add another 1. The result is still not infinite. We can repeat this process for an infinite amount of time and the number is still not infinity.
Sure, individual numbers "on the way" to infinity are not infinite, but that doesn't necessarily disprove the existence of infinity.