W1525 Containment
Prerequisites[edit]
Research[edit]
- Set Theory (Wikipedia)
- Set Theory for Computer Science (Glynn Winskel, University of Cambridge)
Background[edit]
Set Basics[edit]
By the 1930's, through the work of Godel, Church, Turing and others, it was realized that Set Theory relied on an even more basic concept, that of computability. Computer Science continues to be inspired by Set Theory and understanding Set Theory should facilitate your ability to think abstractly. It is, by its nature, independent of yet critical for programming.
A set is an unordered collection of objects. The objects are referred to as elements or members of the set.
Symbols | Definition |
---|---|
The empty set | |
Another way of symbolizing the empty set | |
The set containing the elements | |
is a member of the set | |
is NOT a member of the set | |
ℕ | The set of natural numbers |
ℕ0 | The set of natural numbers with zero |
ℤ | The set of integers (negative, zero, and positive) |
ℝ | The set of real numbers |
The set X is a subset of the set Y | |
The set X is NOT a subset of the set Y |
A set is termed a subset of set iff every element of is an element of . Formally:
Two sets and are equal iff every element of is an element of and vice versa. Formally:
Boolean Algebra of Sets[edit]
Assume set . The following operations are defined:
Symbols | Name | Definition |
---|---|---|
Union | ||
Intersection | ||
Complement |
Set Intersection[edit]
Set Complement[edit]
Experiment[edit]
Getting Started[edit]
Continue from the previous project; we'll be editing all of our files there. Enter into the Sources directory of the project.
john-williams@codermerlin: cd ~/Experiences/W1521/Sources/ScenesShell/
Key Concepts[edit]
Exercises[edit]
References[edit]
- Set Theory (Wikipedia)
- Set Theory for Computer Science (Glynn Winskel, University of Cambridge)