Lines Matching refs:emptyset

23 $$\pdom S \coloneqq \{\, \vec s \in \Z^n \mid S(\vec s) \ne \emptyset \,\}.$$
50 $$\pdom R \coloneqq \{\, \vec s \in \Z^n \mid R(\vec s) \ne \emptyset \,\}.$$
913 i.e., $R \circ R = \emptyset$ or $\domain R \cap \range R = \emptyset$.
1045 = \emptyset
1055 \ne \emptyset
1371 $R^+ \cap \identity \ne \emptyset$.
1412 $R^+ \cap \identity \ne \emptyset$, then, since $T$ is
1414 $T \cap \identity \ne \emptyset$.  This in turn means
1428 For example, if $R = R_1 \cup R_2$ and $R_1 \circ R_2 = \emptyset$,
1438 Note, however, that the condition $R_1 \circ R_2 = \emptyset$
1480 on the condition $R_i \circ R_j = \emptyset$, then there is no problem,
1778 R_{00} & = \emptyset
1787 R_{11} & = \emptyset
1791 In the first iteration, $R_{00}$ remains the same ($\emptyset^+ = \emptyset$).
1871 \domain R_j \subseteq D \text{ or } \domain R_j \cap \range R_i = \emptyset
1877 \range R_j \subseteq D \text{ or } \range R_j \cap \domain R_i = \emptyset
1890 \bigcup_{\shortstack{$\scriptstyle\domain R_j \cap \range R_i = \emptyset$\\
1898 		     $\scriptstyle\range R_j \cap \domain R_i = \emptyset$}}
1904 \bigcup_{\shortstack{$\scriptstyle\domain R_j \cap \range R_i = \emptyset$\\
1905 		     $\scriptstyle\range R_j \cap \domain R_i = \emptyset$}}
1928 \bigcup_{\shortstack{$\scriptstyle\domain R_j \cap \range R_i = \emptyset$}}
1948 \bigcup_{\shortstack{$\scriptstyle\range R_j \cap \domain R_i = \emptyset$}}