| Symbol |
Symbol Name |
Meaning/Definition |
Example |
| \( { \ } \) |
set |
a collection of elements |
\( A = {3,7,9,14}, B = {9,14,28} \) |
| \( A ∩ B \) |
intersection |
objects that belong to set A and set B |
\( A ∩ B = {9,14} \) |
| \( A ∪ B \) |
union |
objects that belong to set A or set B |
\( A ∪ B = {3,7,9,14,28} \) |
| \( A ⊆ B \) |
subset |
A is a subset of B. set A is included in set B. |
\( {9,14,28} ⊆ {9,14,28} \) |
| \( A ⊂ B \) |
proper subset / strict subset |
A is a subset of B, but A is not equal to B. |
\( {9,14} ⊂ {9,14,28} \) |
| \( A ⊇ B \) |
superset |
A is a superset of B. set A includes set B |
\( {9,14,28} ⊇ {9,14,28} \) |
| \( A ⊃ B \) |
proper superset / strict superset |
A is a superset of B, but B is not equal to A. |
\( {9,14,28} ⊃ {9,14} \) |
| \( A \not\subset B \) |
not subset |
set A is not a subset of set B |
\( {9,66} \not\subset {9,14,28} \) |
| \( A \not\supset B \) |
not superset |
set A is not a superset of set B |
\( {9,14,28} \not\supset {9,66} \) |
| \( 2^A \) |
power set |
all subsets of A |
\( \) |
| \( P(A) \) |
power set |
all subsets of A |
\( \) |
| \( A = B \) |
equality |
both sets have the same members |
\( A={3,9,14},B={3,9,14},A=B \) |
| \( A^c \) |
complement |
all the objects that do not belong to set A |
\( \) |
| \( A \backslash B \) |
relative complement |
objects that belong to A and not to B |
\( A = {3,9,14},B = {1,2,3},A\backslash B = {9,14} \) |
| \( A - B \) |
relative complement |
objects that belong to A and not to B |
\( A = {3,9,14},B = {1,2,3},A-B = {9,14} \) |
| \( A ∆ B \) |
symmetric difference |
objects that belong to A or B but not to their intersection |
\( A = {3,9,14},B = {1,2,3},A ∆ B = {1,2,9,14} \) |
| \( A \ominus B \) |
symmetric difference |
objects that belong to A or B but not to their intersection |
\( A = {3,9,14}, B = {1,2,3},A \ominus B = {1,2,9,14} \) |
| \( a∈A \) |
element of, belongs to |
set membership |
\( A={3,9,14}, 3 ∈ A \) |
| \( x\notin A \) |
not element of |
no set membership |
\( A={3,9,14}, 1 \notin A \) |
| \( (a,b) \) |
ordered pair |
collection of 2 elements |
\( \) |
| \( A×B \) |
cartesian product |
set of all ordered pairs from A and B |
\( A×B = {(a,b)|a∈A , b∈B} \) |
| \( |A| \) |
cardinality |
the number of elements of set A |
\( A={3,9,14}, |A|=3 \) |
| \( \# A \) |
cardinality |
the number of elements of set A |
\( A={3,9,14}, \# A=3 \) |
| \( | \) |
vertical bar |
such that |
\( A={x|3 |
| \( \aleph_0 \) |
aleph-null |
infinite cardinality of natural numbers set |
\( \) |
| \( \aleph_1 \) |
aleph-one |
cardinality of countable ordinal numbers set |
\( \) |
| \( Ø \) |
empty set |
Ø = { } |
\( C = {Ø} \) |
| \( \mathbb U \) |
universal set |
set of all possible values |
\( \) |
| \( \mathbb N_0\) |
natural numbers / whole numbers set (with zero) |
\( \mathbb N_0= {0,1,2,3,4,...} \) |
\( 0 ∈ \mathbb N_0 \) |
| \( \mathbb N_1\) |
natural numbers / whole numbers set (without zero |
\( \mathbb N_1= {1,2,3,4,5,...} \) |
\( 6 ∈ \mathbb N_1 \) |
| \( \mathbb Z \) |
integer numbers set |
\( \mathbb Z = {...-3,-2,-1,0,1,2,3,...} \) |
\( -6 ∈ \mathbb Z \) |
| \(\mathbb Q \) |
rational numbers set |
\(\mathbb Q = {x | x=a/b, a,b∈ } \) |
\( 2/6 ∈ \mathbb Q \) |
| \( \mathbb R \) |
real numbers set |
\( \mathbb R = {x | -∞ < x <∞} \) |
\( 6.343434∈ \mathbb R \) |
| \( \mathbb C \) |
complex numbers set |
\( \mathbb C = {z | z=a+bi, -∞ |
\( 6+2i ∈ \mathbb C \) |
