Introduction to Number Systems

A collection of flashcards to help review key concepts and definitions from the lecture on number systems and set theory.

What is a set?

A set is any collection of objects specified in such a way that we can tell whether any given object is or is not in the collection.

What notation is used to describe a set by listing its elements?

Roster Notation.

How is the empty set represented?

The empty set is denoted by {} or ∅.

What does it mean for two sets A and B to be equal?

Two sets A and B are equal if their elements are the same.

What are the natural numbers denoted as?

Natural numbers are denoted as ℕ.

What does the symbol ∈ represent?

The symbol ∈ means 'is an element of'.

How do you indicate that an element is not in a set?

You use the symbol ∉ to indicate that an element is not in a set.

What is set-builder notation?

Set-builder notation describes a set by enclosing a rule within braces.

What is the Union of two sets A and B?

The union of two sets A and B, denoted A ∪ B, consists of elements that are in A or in B.

What is an example of an infinite set?

An example of an infinite set is C = {2, 4, 6, 8, 10, …}.

What does the symbol ∩ represent in set theory?

The symbol ∩ represents the intersection of two sets.

What does it mean when we say A is a subset of B (A ⊆ B)?

A is a subset of B means every element of set A is also an element of set B.

What is a proper subset?

A proper subset A ⊂ B means every element of A is in B, and there is at least one element in B not in A.

What does the symbol U denote?

The symbol U denotes the Universal Set, which contains all elements under consideration.

What happens to the set A when you take its complement A'?

The complement of set A, denoted A', is the set of all elements in the Universal Set U that are not in A.