# Set Symbols

Written by Jerry Ratzlaff on . Posted in Nomenclature & Symbols for Engineering, Mathematics, and Science

## Set Symbols

This is a list of the most common set symbols:

Symbol    Symbol    DefinitionExample
$$\{ \; \}$$ - set, a collection $$A= \{ 1, 2, 3, 4 \}$$ ,  $$B= \{ 3, 4, 5, 6 \}$$
$$\varnothing$$ varnothing empty set $$A=\{ \varnothing\}$$
$$\cap$$ cap intersection, belonging to set A or B $$A\cap B =\{3, 4\}$$
$$\cup$$ cup union, belonging to set A or B $$A\cup B =\{1, 2, 3, 4, 5, 6\}$$
$$\subset$$ subset strict subset, A is subset of B $$\{3, 4\} \subset \{3, 4, 5, 6\}$$
$$\subseteq$$ subseteq subset, A subset of B, A included in B $$\{3, 4\} \subseteq \{3, 4\}$$
$$\nsubseteq$$ nsubseteq not subset, A not subset of B $$\{6, 7\} \nsubseteq \{3, 4, 5, 6\}$$
$$\supset$$ supset strict superset, A superset of B, B not equal to A $$\{3, 4, 5, 6\} \supset \{3, 4\}$$
$$\supseteq$$ supseteq superset, A subset of B, A includes B $$\{3, 4, 5, 6\} \supseteq \{3, 4, 5, 6\}$$
$$\nsupseteq$$ nsupseteq not superset, A not superset of B $$\{3, 4, 5, 6\} \nsupseteq \{6, 7\}$$
$$\uplus$$ uplus multiset union, A plus B = C $$A + B = \{ 1, 2, 3, 4, 5, 6 \}$$
$$\in$$ in belongs to or element of $$B=\{3, 4, 5, 6\}$$ ,  $$3\in B$$
$$\notin$$ notin does not belong to $$B=\{3, 4, 5, 6\}$$ ,  $$1\notin B$$
= - equality, both sets the same A=B $$\{3, 4, 5, 6\} = \{3, 4, 5, 6\}$$
$$-$$ - relative complement, belongs to B but not A $$A-B = \{5, 6\}$$
$$\ominus$$ ominus symmetric difference, belongs to A or B gut no matches $$A \ominus B = \{1, 2, 5, 6\}$$
$$|\;|$$ - cardinality, element of set B  $$|B|=\{3\}$$
$$\mathbb{C}$$ - complex number set $$\mathbb{C} = \{3, \frac{3}{4}, 13.45, -3.56, ... \}$$
$$\mathbb{N_0}$$ - natural number set (with 0) $$\mathbb{N_0} = \{ 0, 1, 2, 3, 4, 5, 6, ... \}$$
$$\mathbb{N_1}$$ - natural number set (without 0) $$\mathbb{N_1} = \{ 1, 2, 3, 4, 5, 6, ... \}$$
$$\mathbb{R}$$ - real number set $$\mathbb{R} = \{3, \frac{3}{4}, 13.45, -3.56, ... \}$$
$$\mathbb{R}^+$$ - real number set, positive $$\mathbb{R} = \{3, \frac{3}{4}, 3.56, ... \}$$
$$\mathbb{R}^-$$ - real number set, negative $$\mathbb{R} = \{-3, -\frac{3}{4}, -3.56, ... \}$$
$$\mathbb{Q}$$ - rational number set $$\mathbb{Q} = \{ \frac{0}{1}, -\frac{1}{8}, \frac{3}{2} \}$$
$$\mathbb{Q}^+$$ - rational number set, positive $$\mathbb{Q} = \{ \frac{0}{1}, \frac{1}{8}, \frac{3}{2} \}$$
$$\mathbb{Q}^-$$ - rational number set, negative $$\mathbb{Q} = \{ -\frac{0}{1}, -\frac{1}{8}, -\frac{3}{2} \}$$
$$\mathbb{U}$$ - universal set $$\mathbb{U} = \{ -3.56, -2, 0, \frac{3}{2}, 13.45, ... \}$$
$$\mathbb{Z}$$ - integer number set $$\mathbb{Z} = \{ ... , -3, -2, -1, 0, 1, 2, 3, ... \}$$
$$\mathbb{Z}^+$$ - integer number set, positive $$\mathbb{Z} = \{ 1, 2, 3, ... \}$$
$$\mathbb{Z}^-$$ - integer number set, negative $$\mathbb{Z} = \{ ... , -3, -2, -1 \}$$
Symbol Symbol Definition Example