Well, 0.9999 does equal 1, because “infinitessimal” equals zero. Or at least it kind of does, the way trans-infinities also equal infinities in many ways. However, they don’t exactly. And infinitessimals don’t equal zero exactly either. (I mean they “equal exactly”, but they have other properties that make them distinct). Integrals, for example, are about adding infinite quantities of infinitessimals to get finite answers.
It’s all about the strange way that there may exist different scales of numbers, separated from one-another by nearly-impassible infinities, which all end up kind of falling into the terms “infinity” and “zero” when looking at them from any particular scale, but which also have their own properties and their own relevance when looking at the big picture. (And when using methods that take away the intractability of examining them head on.)
So yes, 0.9999… does equal 1. Maybe it “completely” equals 1 if the concept of one minus infitessimal doesn’t hold any interesting properties. However, it also might not quite equal 1, in that there might be such properties. (For example, 1+infinitessimal to the infinite power equals e).
But, if you ask most mathematical philosophers, they’d rather not talk about infinities at all. The subject is quite closed to intuition (and intractable head-on), and they’re right it is often much better to talk about it from a different angle. For example, usually they’ll say that we can never perform any infinite operations (such as infinite additions), and that we only take the limits of them approaching infinite procedures. A useful, practical way of looking at things. But I do not believe it is often the best or philosophically accurate way to treat the topic. For example, would anyone like to start talking about Godel? (Actually, don’t answer that, I’m about to go start a thread in GD).
NOO!!! Besides entertainmnet value, there is IMMENSE REASON that a society cannot just devolve to answer every question by referencing some previous answer. We have to keep reexamining questions anew and actively continuing discussion (even if we don’t add anything on the third time we reanswer the question, but on the 20th). This is a huge threat that is dawning on the information age.