50 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

115. The base of a radix notation may be thought of either
without reference to the notation of which it is the base or
with reference to that notation. In the former case it is use-
ful to represent it by a special (visual) symbol and a special
(spoken) name; thus the base of the decimal system by the
symbol ‘¥ and the name ten, the base of the sexidenal system
by the symbol [0 and the name sixteen.

With reference to the system of notation the base is repre-
sented by the symbol 10, whatever the system. It would
seem wise that the base should also be represented by a name
which should be independent of the particular system used.
The name wunty, analog of twenty, thirty, etc., from one point
of view and of one hundred, one thousand, one million, etc.,
from another point of view, seems appropriate.

Similarly, just as the double of the base is represented in
every system whose base is large enough by 20, the triple by
30, and so on, it would seem wise to represent these multiples
always by the same names, independent of the system. The
names twenty, thirty, etc., seem best, especially if we wish to
make the learning of a new system as easy as possible.

Similarly also, as the second power of the base is always
represented by the symbol 100, the third power by 1000, and
so on, it would seem wise to represent these powers always
by the same names.

Thus the names wunty, twenty, thirty, etc., wun hundred,
tu hundred, etc., wun thousand, etc., will respectivly repre-
sent different numbers in different systems.

116. If we wish to employ a base larger than ten, we may,
instead of using new symbols, use letters for the extra digits.
Thus with 2° for base we may count as follows:

L e AL AB CDEFGHKLM,
N0 S T UV, WX, X, 10,

The best way to read a number written in such a notation,
one that uses letters, would probably be to read its digits
successivly ; thus 6023M would be read “ six, o, tu, three, em,”
instead of “‘ sixty thousand tu hundred thirty em.”