Central Proposition: If there is a typographical rule which tells how certain digits are to be shifted, changed, dropped, or inserted in any number represented decimally, then this rule can be rep resented equally well by an arithmetical counterpart which in volves arithmetical operations with powers of 10 as well as addi tions, subtractions, and so forth. More briefly: Typographical rules for manipulating numerals are actually arithmetical rules for operating on numbers