[CG] Re: Peirce's 1870 “Logic of Relatives”

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 11.7 https://inquiryintoinquiry.com/2014/05/05/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 11.7 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, We come now to the special cases of dyadic relations known as functions. It will serve a dual purpose in the present exposition to take the class of functions as a source of object examples for clarifying the more abstruse concepts of Relation Theory. To begin, let us recall the definition of a “local flag” L_{a @ j} of a k-adic relation L. Display 1 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… For a dyadic relation L ⊆ X × Y the notation for local flags can be simplified in two ways. First, the local flags L_{u @ 1} and L_{v @ 2} are often more conveniently notated as L_{u @ X} and L_{v @ Y}, respectively. Second, the notation may be streamlined even further by making the following definitions. Display 2 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… In light of these conventions, the local flags of a dyadic relation L ⊆ X × Y may be comprehended under the following descriptions. Display 3 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… The following definitions are also useful. Display 4 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… A sufficient illustration is supplied by the earlier example E. Figure 35. Dyadic Relation E https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-30.j… Figure 36 shows the local flag E_{3 @ X} of E. Figure 36. Local Flag E_{3 @ X} https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-36.j… Figure 37 shows the local flag E_{2 @ Y} of E. Figure 37. Local Flag E_{2 @ Y} https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-37.j… Regards, Jon