Volume 1 / Part 4 — *184. THE PRODUCT OF TWO RELATION-NUMBERS.
Reading edition
*184. THE PRODUCT OF TWO RELATION-NUMBERS.
Summary of *184.
The propositions of this number are for the most part analogous to those of the propositions of *113 which are concerned with . Those of *113 which are concerned with have their analogues in *166. We put
*184·01.
*184·02.
*184·03.
We prove that is only zero when one of its factors is zero (*184·16); we prove the associative law (*184·31), and the distributive law in the forms
*184·33.
*184·35.
and we prove (*184·4). Also we extend the distributive law to the case where one of the summands is , i.e. we prove
*184·41.
*184·42.
and the connection of cardinal and ordinal multiplication is given by
*184·5.
*184·01.
*184·02.
*184·03.
*184·1.
The proofs of the following propositions are omitted, since they are analogous to those of the corresponding propositions of *113.
*184·11.
*184·111.
*184·12.
*184·13.
*184·14.
*184·15.
*184·16.
*184·2.
*184·21.
Dem.
*184·3.
Dem.
*184·31.
Dem.
*184·32.
*184·33.
Dem.
*184·34.
Dem.
*184·35.
The proof proceeds as in *184·31.
*184·4.
Dem.
*184·41.
Dem.
*184·42.
*184·5.
Dem.