In the Christian era the years are simply distinguished by the cardinal numbers; those before Christ being marked B.C. (Before Christ), or A.C. (Ante Christum), and those after Christ A.D.
The operations of addition and multiplication of two given cardinal numbers can be defined by taking two classes a and 13, satisfying the conditions (1) that their cardinal numbers are respectively the given numbers, and (2) that they contain no member in common, and then by defining by reference to
With these definitions it is now possible to prove the following six premisses applying to finite cardinal numbers, from which Peano 2 has shown that all arithmetic can be deduced i.
Thus, while arithmetic may be defined as that branch of deductive reasoning concerning classes and relations which is concerned with the establishment of propositions concerning cardinal numbers, it must be added that the introduction of cardinal numbers makes no great break in this general science.
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