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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 11.10 https://inquiryintoinquiry.com/2014/05/07/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 11.10 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, A dyadic relation F ⊆ X × Y which qualifies as a function f : X → Y may then enjoy a number of further distinctions. Definitions https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… For example, the function f : X → Y shown below is neither total nor tubular at its codomain Y so it can enjoy none of the properties of being surjective, injective, or bijective. Figure 40. Function f : X → Y https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-40.j… An easy way to extract a surjective function from any function is to reset its codomain to its range. For example, the range of the function f above is Y' = {0, 2, 5, 6, 7, 8, 9}. If we form a new function g : X → Y' that looks just like f on the domain X but is assigned the codomain Y', then g is surjective, and is described as a mapping onto Y'. Figure 41. Function g : X → Y' https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-41.j… The function h : Y' → Y is injective. Figure 42. Function h : Y' → Y https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-42.j… The function m : X → Y is bijective. Figure 43. Function m : X → Y https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-43.j… Regards, Jon