数学

\[\pi_{M}:\prod_{\lambda\in\lambda}A_{\lambda}\rightarrow\prod_{\mu\in M}A_{\mu},\left(x_{\lambda}\right)_{\lambda\in\Lambda}\mapsto\left(x_{\mu}\right)_{\mu\in M}\]

\[\prod_{\lambda\in\Lambda}A_{\lambda}=\left\{ f:\Lambda\rightarrow\bigcup_{\lambda\in\Lambda}A_{\lambda};f\left(\lambda\right)\in A_{\lambda},\lambda\in\Lambda\right\} \]

\[\left(\right)=\emptyset\]

\[\left(a_{k}\right)_{k\in I}=\left\{ \left(i,a_{i}\right);i\in I\right\} \]

\[\left(a_{1},b_{1}\right)=\left(a_{2},b_{2}\right)\Leftrightarrow a_{1}=a_{2}\land b_{1}=b_{2}\]

\[x\sim y\Leftrightarrow\exists P\in\mathcal{P},x\in P\land y\in P\]

\[\left\{ a,b,c\right\} =\left\{ a\right\} \cup\left\{ b,c\right\} \]

\[\bigcup\mathcal{A}=\bigcup_{\lambda\in\Lambda}A_{\lambda}=\left\{ x;\exists\lambda\in\Lambda,x\in A_{\lambda}\right\} \]

\[\left\{ A_{\lambda}\right\} _{\lambda\in\Lambda}\]

\[A^{c}:=X\setminus A\]

\[A\cap B=\emptyset\]

\[A\cap B=\emptyset\Leftrightarrow\left(A\times B\right)\cap\Delta_{X}=\emptyset\]

\[\Delta_{X}=\left\{ \left(x,y\right)\in X\times X;x=y\right\} \subseteq X^{2}\]

$\left\{ A;A\notin A\right\} $は集合ではない

\[\emptyset\subseteq A\]

\[2^{A}\]

\[A=B\Leftrightarrow A\subseteq B\land A\supseteq B\]

\[\emptyset=\left\{ \right\} \]

\[\left\{ a,b,c\right\} \]

\[a\in A\]