Thread: JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15704 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15705
Peircers, Submitted for your approval, two ways of looking at the “divisor of” relation, one of the most fundamental examples of a binary (dyadic or two-place) relation in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers that corresponds 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 notation is i|j. Table 1. Elementary Relatives for the “Divisor Of” Relation ☞http://inquiryintoinquiry.com/elementary-relatives-for-the-divisor-of-relation/ 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 here for ease of reading.) Table 2. Logical Matrix for the “Divisor Of” Relation ☞http://inquiryintoinquiry.com/logical-matrix-for-the-divisor-of-relation/ Just as matrices in linear algebra represent linear transformations, these logical arrays and matrices represent logical transformations. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ isw: http://intersci.ss.uci.edu/wiki/index.php/JLA oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
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