Changes

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Peirce is well aware that it is not at all necessary to arrange the elementary relatives of a relation into arrays, matrices, or tables, but when he does so he tends to prefer organizing 2-adic relations in the following manner:

Peirce is well aware that it is not at all necessary to arrange the

elementary relatives of a relation into arrays, matrices, or tables,

but when he does so he tends to prefer organizing 2-adic relations

in the following manner:

  a:b +  a:b +  a:c +

a\!:\!a & a\!:\!b & a\!:\!c

b\!:\!a & b\!:\!b & b\!:\!c

c\!:\!a & c\!:\!b & c\!:\!c

  b:a +  b:b  +  b:c  +

For example, given the set <math>X = \{ a, b, c \},\!</math> suppose that we have the 2-adic relative term <math>\mathit{m} = {}^{\backprime\backprime}\, \text{marker for}\, \underline{~~~~}\, {}^{\prime\prime}</math> and

the associated 2-adic relation <math>M \subseteq X \times X,</math> the general pattern of whose common structure is represented by the following matrix:

{| align="center" cellpadding="6" width="90%"

 

| align="center" |

For example, given the set X = {a, b, c}, suppose that

we have the 2-adic relative term m = "marker for" and

M \quad = \quad

M_{aa}(a\!:\!a) & M_{ab}(a\!:\!b) & M_{ac}(a\!:\!c)

 

M_{ba}(b\!:\!a) & M_{bb}(b\!:\!b) & M_{bc}(b\!:\!c)

  M =

 

M_{ca}(c\!:\!a) & M_{cb}(c\!:\!b) & M_{cc}(c\!:\!c)

  M_aa a:a +  M_ab a:b +  M_ac a:c +

 

  M_ba b:a +  M_bb b:b +  M_bc b:c +

 

  M_ca c:a +  M_cb c:b +  M_cc c:c

It has long been customary to omit the implicit plus signs

It has long been customary to omit the implicit plus signs

in these matrical displays, but I have restored them here

in these matrical displays, but I have restored them here