sets

Summary

Set builder for infinite sets, similar to quantifications

• for all x in the domain which fulfills the predicate

Rules of set operators, corollary of the laws of boolean algebra

Subset and proper subset

Concept

Properties of sets

• no ordering
• no repetition

Set notation and operations

Domain expansion (Theorem 2.1)

Empty set

• there is nothing in the empty set

The empty set is a subset of every set (Corollary 2.2)

cont. there is a unique empty set (Corollary 2.3)

Power set

• set of all the possible subsets of its input

a set can be an element of another set, similar to nested arrays

Application

Set statements

Power sets

• the empty set is always an element of the power set
• use the size formula to check