  In this paper, we present a comprehensive system for the treatment of the
topic of limits--conceptually, computationally, and formally. The system
addresses fundamental linguistic flaws in the standard presentation of limits,
which attempts to force limit discussion into the language of individual real
numbers and equality. The system of near-numbers properly fit the context of
limits, allowing precise and unambiguous notation in limit computation. More
importantly, the near-numbers are a set of concrete mathematical objects that
provide a scaffold both for building an accurate intuitive understanding of the
limit concept and for connecting that understanding to the formal definition of
the limit.
