Jon, List Thank you for reminding me of the definition of a group that I have taught for 45 years ... I think you work with the permutations of symmetrical groups that do not fit well with the interdependence of categories and which make us go out of the Peircian theory, which is not forbidden as long as we point it out. I'll look at the use you make of them when you've answered my previous questions with something other than a stream of links and the definition of a group! (my Ph.D. Math is on Abelian Groups)... formulating my questions correctly takes me time, especially to grasp your thought... I would like a reciprocal... I always thought that you had the capacity to do it without giving up your certainties, but I must say that today I am disappointed... Regards,
Robert Marty Honorary Professor ; Ph.D. Mathematics ; Ph.D. Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le ven. 13 août 2021 à 00:20, Jon Awbrey <[email protected]> a écrit : > Cf: Semiotics, Semiosis, Sign Relations • Comment 3 > > https://inquiryintoinquiry.com/2021/08/12/semiotics-semiosis-sign-relations-comment-3/ > > All, > > It helps me to compare sign relations with my other favorite class > of triadic relations, namely, groups. Applications of mathematical > groups came up just recently in the Laws of Form discussion group, > so it will save a little formatting time to adapt the definition > used there. > > Cf: Animated Logical Graphs • 60 > https://inquiryintoinquiry.com/2021/02/21/animated-logical-graphs-60/ > > Definition 1. A group (G, ∗) is a set G together with > a binary operation ∗ : G × G → G satisfying the following > three conditions. > > 1. Associativity. > For any x, y, z in G, we have (x ∗ y) ∗ z = x ∗ (y ∗ z). > > 2. Identity. > > There is an identity element 1 in G such that for all g in G, > we have 1 ∗ g = g ∗ 1 = g. > > 3. Inverses. > Each element has an inverse, that is, for each g in G, > there is some h in G such that g ∗ h = h ∗ g = 1. > > Regards, > > Jon > > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to > [email protected] with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the > message and nothing in the body. More at > https://list.iupui.edu/sympa/help/user-signoff.html . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell. >
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