Inquiry Blog http://inquiryintoinquiry.com/2015/12/08/relations-their-relatives-16/ http://inquiryintoinquiry.com/2015/12/10/relations-their-relatives-17/ http://inquiryintoinquiry.com/2015/12/12/relations-their-relatives-18/ http://inquiryintoinquiry.com/2015/12/22/relations-their-relatives-19/
Peirce List JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18101 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/18105 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/18107 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/18121 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/18208 Helmut, List, There's a much better formatted copy of this message on my inquiry blog: http://inquiryintoinquiry.com/2016/01/04/relations-their-relatives-20/ We have been considering special properties that a dyadic relations may have, in particular, the following two “symmetry properties”. A dyadic relation L is “symmetric” if (x, y) being in L implies that (y, x) is in L. A dyadic relation L is “asymmetric” if (x, y) being in L implies that (y, x) is not in L. The first thing to understand about any symmetry of any relation is that it is a property of the whole relation, the whole set of tuples, not a property of individual tuples. Many properties of dyadic relations can be made visually evident by arranging their ordered pairs in 2-dimensional arrays. Let's do this for our initial sample of biblical brothers, using the first three letters of their names as row and column labels. The relation B indicated by “brother of” is a symmetric relation. The ordered pairs of B are given below. http://s0.wp.com/latex.php?latex=\begin{array}{l|*{8}{c}}+B+%26+\rm{Abe}+%26+\rm{Ben}+%26+\rm{Cai}+%26+\rm{Esa}+%26+\rm{Isa}+%26+\rm{Ish}+%26+\rm{Jac}+%26+\rm{Jos}+\\[2pt]+\hline+\\[2pt]+\rm{Abe}+%26+\centerdot+%26%26+\rm{Abe%3ACai}+%26%26%26%26%26\\[12pt]+\rm{Ben}+%26%26+\centerdot+%26%26%26%26%26%26+\rm{Ben%3AJos}+\\[12pt]+\rm{Cai}+%26+\rm{Cai%3AAbe}+%26%26+\centerdot+%26%26%26%26%26\\[12pt]+\rm{Esa}+%26%26%26%26+\centerdot+%26%26%26+\rm{Esa%3AJac}+%26\\[12pt]+\rm{Isa}+%26%26%26%26%26+\centerdot+%26+\rm{Isa%3AIsh}+%26%26\\[12pt]+\rm{Ish}+%26%26%26%26%26+\rm{Ish%3AIsa}+%26+\centerdot+%26%26\\[12pt]+\rm{Jac}+%26%26%26%26+\rm{Jac%3AEsa}+%26%26%26+\centerdot+%26\\[12pt]+\rm{Jos}+%26%26+\rm{Jos%3ABen}+%26%26%26%26%26%26+\centerdot++\end{array}&bg=ffffff&fg=000000&s=-1&zoom=2 The relation E indicated by “elder brother of” is an asymmetric relation. The ordered pairs of E are given below. http://s0.wp.com/latex.php?latex=\begin{array}{l|*{8}{c}}+E+%26+\rm{Abe}+%26+\rm{Ben}+%26+\rm{Cai}+%26+\rm{Esa}+%26+\rm{Isa}+%26+\rm{Ish}+%26+\rm{Jac}+%26+\rm{Jos}+\\[2pt]+\hline+\\[2pt]+\rm{Abe}+%26+\centerdot+%26%26%26%26%26%26%26\\[12pt]+\rm{Ben}+%26%26+\centerdot+%26%26%26%26%26%26\\[12pt]+\rm{Cai}+%26+\rm{Cai%3AAbe}+%26%26+\centerdot+%26%26%26%26%26\\[12pt]+\rm{Esa}+%26%26%26%26+\centerdot+%26%26%26+\rm{Esa%3AJac}+%26\\[12pt]+\rm{Isa}+%26%26%26%26%26+\centerdot+%26%26%26\\[12pt]+\rm{Ish}+%26%26%26%26%26+\rm{Ish%3AIsa}+%26+\centerdot+%26%26\\[12pt]+\rm{Jac}+%26%26%26%26%26%26%26+\centerdot+%26\\[12pt]+\rm{Jos}+%26%26+\rm{Jos%3ABen}+%26%26%26%26%26%26+\centerdot++\end{array}&bg=ffffff&fg=000000&s=-1&zoom=2 Regards, and Happy 2016 = 2⁵3²7 = 32 • 63 = 2⁵(2⁶ -1) = 2¹¹ - 2⁵ = 11111100000 (in binary) 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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