集合の基本
要素 | \( \Large \in \) | \in | | \( \Large \ni \) | \ni |
包含 | \( \Large \subset \) | \subset | | \( \Large \supset \) | \supset |
\( \Large \subseteq \) | \subseteq | | \( \Large \supseteq \) | \supseteq |
| \( \Large \prec \) | \prec | | \( \Large \succ \) | \succ |
\( \Large \preceq \) | \preceq | | \( \Large \succeq \) | \succeq |
空集合 | \( \Large \emptyset \) | \emptyset |
内包的記法
\( \displaystyle \Large A = \left\{ \frac{n}{m} \middle| n,m \in \mathbb{R} \right\} \)
A = \left\{ \frac{n}{m} \middle| n,m \in \mathbb{R} \right\}
集合演算
和集合 | \( \Large \cup \) \cup | \( \displaystyle\Large \bigcup^n_{k=1}A_k \) \bigcup^n_{k=1}A_k |
共通部分 | \( \Large \cap \) \cap | \( \displaystyle\Large \bigcap^n_{k=1}A_k \) \bigcap^n_{k=1}A_k |
差集合 | \( \Large \setminus \) \setminus |
対称差 | \( \Large \bigtriangleup \) \bigtriangleup | \( \Large \ominus \) \ominus | \( \Large \oplus \) \oplus |
直積 | \( \Large \times \) \times | \( \displaystyle\Large \prod^n_{k=1} A_k \) \prod^n_{k=1} A_k |
冪集合 | \( 2^A \) | 2^A |
\( \Large \mathbb{P}(A) \) | \mathbb{P}(A) |
\( \Large \mathfrak{P}(A) \) | \mathfrak{P}(A) |
\( \Large \mathfrak{Pow}(A) \) | \mathfrak{Pow}(A) |
\( \Large \cal{P}(A) \) | \cal{P}(A) |
\( \Large \prod (A) \) | \prod (A) |
\( \Large \mathrm{Power}(A) \) | \mathrm{Power}(A) |
\( \Large \wp(A) \) | \wp(A) |
組・順序対
順序対 | \( \Large \langle x,y \rangle \) | \langle x,y \rangle |
組 | \( \Large \langle x_1,x_2,\dots,x_n \rangle \) | \langle x_1,x_2,\dots,x_n \rangle |