>>12325802I know that 0.999... = 1 and was playing devil's advocate there.
You might benefit from reading this:
https://www.lesswrong.com/posts/i7oNcHR3ZSnEAM29X/standard-and-nonstandard-numbers(No, I'm not in Yudkowsky's "cult," I just googled some relevant terms and it so happened the guy had written an accessible explanation of the kind of difficulties you encounter in defining what the natural numbers are.)
Also, in the future, if you find yourself arguing about 0.999..., I suggest not spending so much time arguing about the decimal representations of numbers, and focus on what the representations are supposed to mean. An important prerequisite to understanding 0.999... = 1 is understanding that these are just ways of naming numbers, and a single number can have two different names.
Another thing to be aware of is that that there are number systems that contain nonzero infinitesimals -- numbers with a smaller absolute value than any nonzero rational number. So there are number systems where there's a number greater than each of 0.9, 0.99, 0.999, and so on, but less than 1, because you can take 1 and subtract a positive infinitesimal. It's just that these number systems are different systems than the usual one we normally use, the real numbers. In the real numbers there are no nonzero infinitesimals.
