Set theory symbols
Before moving forward with category theory, let's get familiar with the symbols of set theory:
Symbol | Symbol name | Meaning/definition | Example |
{ } | Set | A collection of objects (also known as elements) | A = {5,6,7,8}, B = {5,8,10} |
| | Such that | So that | A = {x | x ∈ ℝ, x<0} |
A∩B | Intersection | Objects that belong to set A and set B | A ∩ B = {5,8} |
A∪B | Union | Objects that belong to set A or set B | A ∪ B = {5,6,7,8,10} |
A⊆B | Subset | A is a subset of B. Set A is included in set B | {5,8,10} ⊆ {5,8,10} |
A⊂B | Proper subset / Strict subset | A is a subset of B, but A is not equal to B | {5,8} ⊂ { 5,8,10} |
A⊄B | Not subset | Set A is not a subset of set B | {8,15} ⊄ {8,10,25} |
a∈A | Element of | Set membership | A ={5,10,15}, 5 ∈ A |
x∉A | Not element of | No set membership | A ={5,10,15}, 2 ∉ A |
(a,b) | Ordered pair | A collection of 2 elements | |
A×B | Cartesian product | A set of all ordered pairs from A and B | |
|A| | Cardinality | The number of elements of set A | A ={5,10,15}, |A|=3 |
Ø | Empty set | Ø = {} | A = Ø |
↦ | Maps to | f: a ↦ b means the function f maps from the element a to the element b | f: a ↦... |
