1. Decimal-Metric Number-phrases.
RDA starts from the necessity to represent real-world
collections
of
items which requires the notion of
number-phrases,
that is both a
denominator to record the
kind
of items and a
numerator to record the
number
of items. However, if the real-world processes are based on the
cardinal
aspect, one-to-one correspondances, the paper procedures are based on
the
ordinal
aspect, counting. Also, signed numerators are introduced almost from
the start. There are then two issues: The first issue is with
large
collections which force us
to bunch the items and then count the bunches. This
gives us
decimal number-phrases and is best seen
in the context of the
metric
system with
money
as its embodiment.
2. Approximation.
The second issue comes up when we deal with
amounts
of stuff as opposed to
collections of items, for
instance water as opposed to rocks. This forces us to introduce the
idea of
approximation.
While this is usually done almost as an afterthought, here, inasmuch as
arithmetic is to represent
real-world situations,
the idea of
approximation
is totally natural and, as a prequel to
Lagrange
Differential Calculus, an absolute must.
3. Arithmetic Functions.
They occur quite naturally once the distinction has been made between
states
and
actions. Strictly speaking, this
may not be necessary to a "profound
understanding of fundamental arithmetic". However, it certainly
facilitates matters and of course helps considerably the flow in the
framework of
A2DC.
4. Comparisons and
Operations. This is probably the more conventional part of
RDA except that it turns out that the four operations are best seen as
unary operators, that is
of course, as
functions.