*41. THE PRODUCT AND SUM OF A CLASS OF RELATIONS.
Project Gutenberg EPUB3 edition
Whitehead, Alfred North and Russell, Bertrand
Summary of *41.
The propositions to be given in this number, down to *41·3 exclusive, are the analogues of those of *40, excluding those from *40·3 onwards, which have no analogues. Proofs will not be given, in this number, when they are exactly analogous to those of propositions with the same decimal part in *40. The smaller importance of and , as compared with and , is illustrated by the smaller number of propositions in *41 as compared with *40.
Our definitions are
*41·01.
*41·02.
Of the propositions preceding *41·3, which are analogues of propositions in *40, the only two that are frequently used are
*41·13.
*41·151.
Of the remaining propositions of this number, which have no analogues in *40, the most important are *41·43·44·45, namely These propositions are constantly required in the theory of selections (Part II, Section D) and in relation-arithmetic. Most of the other propositions of this number are used only once or not at all.
*41·01.
*41.02.
*41·1.
*41·11.
*41·12.
*41·13.
*41·14.
*41·141.
*41·15.
*41·151.
*41·16.
*41·161.
*41·17.
*41·171.
*41·18.
*41·181.
*41·19.
*41·2.
*41·21.
*41·22.
*41·221.
*41·23.
*41·24.
*41·25.
*41·26.
*41·27.
*41·3.
Dem.
*41·31.
*41·32.
*41·33.