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Directory talk:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 02:08, 7 May 2009
, 02:08, 7 May 2009→Commentary Note 12.5
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="100" | <math>(\mathfrak{L}^\mathfrak{W})_u ~=~ \prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_x}</math>
| height="80" | <math>(\mathfrak{L}^\mathfrak{W})_x ~=~ \prod_{p \in X} \mathfrak{L}_{xp}^{\mathfrak{W}_p}</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="100" |
| height="80" |
<math>
<math>
(\mathfrak{S}^\mathfrak{L})_{uv} ~=~
(\mathfrak{S}^\mathfrak{L})_{xy} ~=~
\prod_{x \in X} \mathfrak{S}_{ux}^{\mathfrak{L}_{xv}}
\prod_{p \in X} \mathfrak{S}_{xp}^{\mathfrak{L}_{py}}
</math>
</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="100" |
| height="80" |
<math>
<math>
(\mathfrak{S}^\mathfrak{L})_{xp} ~=~
\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}}
</math>
</math>
|}
|}
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| height="100" |
| height="80" |
<math>
<math>
(\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_u ~=~
((\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_x ~=~
\prod_{x \in X} (\mathfrak{S}^\mathfrak{L})_{ux}^{\mathfrak{W}_x}
(\mathfrak{S}^{\mathfrak{L}\mathfrak{W}})_x
</math>
|}
{| align="center" cellspacing="6" width="90%"
| height="80" |
<math>
(\mathfrak{S}^\mathfrak{L})^\mathfrak{W})_x ~=~
\prod_{p \in X} (\mathfrak{S}^\mathfrak{L})_{xp}^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}})^{\mathfrak{W}_p} ~=~
\prod_{p \in X} (\prod_{q \in X} \mathfrak{S}_{xq}^{\mathfrak{L}_{qp}\mathfrak{W}_p})
</math>
</math>
|}
|}