Let X denote 0.999... (written just like that). It does follow from certain standard definitions that X=1. It is possible to use other non-absurd definitions and have X<1 but it is hardly worth it, for example you have to either accept that X+X=1+X or say that the left hand side does not make sense. It is not an exaggeration that you can start with 0.999...=1 as a basic definition, combine that with reasonable rules of arithmetic and recover some of the standard definitions as consequences. This approach is rigorous and valid but not popular (with good reason) Two respectable texts using this approach are  J. F. Ritt, Theory of Functions, 1946 (in full) and  M. Rosenlicht, Introduction to Analysis (in outline). The first is hard to find, the second is reprinted by Dover. In short, it is true by definition or by easy consequence of the definitions. The distinctions are subtle and it would be a mistake to discuss them in the high school curriculum (or 99.993% of the undergraduate curriculum.)  One could discuss them in Wikipedia but it would be highly upsetting to lots of people including students, former students, teachers.