Set Symbols

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

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Set Symbols

This is a list of the most common set symbols:

SymbolDefinitionExample
\(\{ \; \}\) set, a collection \(A= \{ 1, 2, 3, 4 \}\) ,  \(B= \{ 3, 4, 5, 6 \} \)
\(\varnothing\) empty set \(A=\{ \varnothing\} \)
\(\cap\) intersection, belonging to set A or B \(A\cap B =\{3, 4\}\)
\(\cup\) union, belonging to set A or B \(A\cup B =\{1, 2, 3, 4, 5, 6\}\)
\(\subset\) strict subset, A is subset of B \(\{3, 4\} \subset \{3, 4, 5, 6\}\)
\(\subseteq\) subset, A subset of B, A included in B \(\{3, 4\} \subseteq \{3, 4\}\)
\(\nsubseteq\) not subset, A not subset of B \(\{6, 7\} \nsubseteq \{3, 4, 5, 6\}\)
 \(\supset\) strict superset, A superset of B, B not equal to A \(\{3, 4, 5, 6\} \supset \{3, 4\}\)
 \(\supseteq\) superset, A subset of B, A includes B \(\{3, 4, 5, 6\} \supseteq \{3, 4, 5, 6\}\)
\(\nsupseteq\) not superset, A not superset of B \(\{3, 4, 5, 6\} \nsupseteq \{6, 7\}\)
\(\uplus\) multiset union, A plus B = C \(A + B = \{ 1, 2, 3, 4, 5, 6 \}\)
\(\in\) belongs to or element of \(B=\{3, 4, 5, 6\}\) ,  \(3\in B\)
\(\notin\) 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 \(A-B = \{5, 6\}\)
\(\ominus\) 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 \(\mathbb{Z} = \{ ... , -3, -2, -1 \}\)