12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Thursday November 07, 2024
Jump to navigationJump to searchDirectory talk:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 16:00, 1 December 2015
, 16:00, 1 December 2015→Operational Representation: + next clause
|-
|-
|
|
<math>\begin{matrix}
<math>\begin{array}{c}
f_{1}
\\[4pt]
\\[4pt]
f_2
f_2
\\[4pt]
\\[4pt]
f_8
f_8
\end{matrix}\!</math>
\end{array}\!</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
Recognizing that <math>a\!:\!a + b\!:\!b + c\!:\!c\!</math> is the identity transformation otherwise known as <math>\mathit{1},\!</math> the 2-adic relative term <math>m = {}^{\backprime\backprime}\, \text{marker for}\, \underline{~ ~ ~}\, {}^{\prime\prime}~\!</math> can be parsed as an element <math>\mathit{1} + a\!:\!b + b\!:\!c + c\!:\!a\!</math> of the so-called ''group ring'', all of which makes this element just a special sort of linear transformation.
Recognizing that <math>a\!:\!a + b\!:\!b + c\!:\!c\!</math> is the identity transformation otherwise known as <math>\mathit{1},\!</math> the 2-adic relative term <math>m = {}^{\backprime\backprime}\, \text{marker for}\, \underline{~ ~ ~}\, {}^{\prime\prime}~\!</math> can be parsed as an element <math>\mathit{1} + a\!:\!b + b\!:\!c + c\!:\!a\!</math> of the so-called ''group ring'', all of which makes this element just a special sort of linear transformation.
Up to this point, we are still reading the elementary relatives of the form <math>i\!:\!j</math> in the way that Peirce read them in logical contexts:
==Logical Cacti==
==Logical Cacti==
