[CG] Re: Relations & Their Relatives

Relations & Their Relatives • 3 • https://inquiryintoinquiry.com/2024/08/02/relations-their-relatives-3-a/ All, Here are two ways of looking at the divisibility relation, a dyadic relation of fundamental importance in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers corresponding to the relative term, “divisor of”. Thus, the ordered pair i:j appears in the relation if and only if i divides j, for which the usual mathematical notation is “i|j”. Table 1. Elementary Relatives for the “Divisor Of” Relation • https://inquiryintoinquiry.files.wordpress.com/2015/02/elementary-relatives… Table 2 shows the same information in the form of a logical matrix. This has a coefficient of 1 in row i and column j when i|j, otherwise it has a coefficient of 0. (The zero entries have been omitted for ease of reading.) Table 2. Logical Matrix for the “Divisor Of” Relation • https://inquiryintoinquiry.files.wordpress.com/2015/02/logical-matrix-for-t… Just as matrices in linear algebra represent linear transformations, logical arrays and matrices represent logical transformations. Resources — Relation Theory • https://oeis.org/wiki/Relation_theory Triadic Relations • https://oeis.org/wiki/Triadic_relation Sign Relations • https://oeis.org/wiki/Sign_relation Survey of Relation Theory • https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/ Peirce's 1870 Logic Of Relatives • https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview Regards, Jon cc: https://www.academia.edu/community/VBZ14o