Introduction to Set Theory

These flashcards cover key concepts and definitions from the lecture on set theory, enabling effective review and preparation for exams.

What is a basic human impulse mentioned in the lecture that relates to organizing information?

The impulse to sort or classify things into sets.

Why is organizing elements into sets beneficial?

It helps deal with large quantities of information.

What is a 'set' as defined in the lecture?

A collection of objects whose contents can be clearly determined.

How are elements or members defined in a set?

They are the objects contained within the set.

Is the order of elements in a set important?

No, the order of elements in a set is not important.

What capital letter is used to represent the set of days of the week?

SETW.

What is the roster method in set theory?

It lists the members of a set if they are small enough.

What symbol is used to designate that the enclosed elements form a set?

Braces ({}).

What is an empty set?

A set that contains no elements.

What are two symbols used to represent an empty set?

Empty braces {} and a circle with a line through it (∅).

What is set builder notation?

A way to define a set using a variable and a condition that elements must meet.

How do you represent a positive odd number less than 10 in set builder notation?

Set O is the set of all x such that x is a positive odd number less than 10.

What is the cardinality of a set?

The number of distinct elements in a set.

What does it mean for two sets to be equal?

They contain exactly the same elements regardless of order or repetition.

What is an equivalent set?

Two sets are equivalent if they have the same number of elements.

What are finite and infinite sets?

A finite set has a cardinal number that is zero or a natural number; an infinite set does not have a final element.

What does the notation 'x ∈ A' mean?

x is an element of set A.

What does the notation 'x ∉ A' mean?

x is not an element of set A.

What are the two key properties of the word 'and' in set conditions?

It requires elements to satisfy both conditions.