Usually the concept of a limit, which assigns a meaning to 0.999..., isn't studied until calculus. There are approaches to mathematics that avoid infinite cons

Usually the concept of a limit, which assigns a meaning to 0.999..., isn't studied until calculus. There are approaches to mathematics that avoid infinite constructions, and a "strict finitist" would not assign 0.999... a meaning. The stunning success of limit based mathematics makes finitism a fringe philosophy. Remember, class, for every epsilon there is a delta.