RESUMEN
Some new theorems have been propounded for the
numbers (M - 1), as they relate to other numerals, through the basic
arithmetical operations, at different bases M. For some reason, we give the
proof of the theorems for the case M = 10 using mathematical induction, and by
Peano’s fifth axiom make our generalizations. Comments are made in respect of
the numbers (M - 1), (in this case 9). Apart from our theorem facilitating
mathematical operations, evidences have also been given, from different sources
of the interesting properties of this class of numbers, represented in our own
case by the numeral 9. The theorems neither violate the divisibility rule for 9
nor are they a consequence of it. From smmetry, a suggestion is made in respect
of the possible origin of the numeration in base 10, and the case of a ten
dimensional Universe reconsidered.