1. Sets Flashcards
What is a set?
A well defined collection of objects, where the objects are called the elements or members of the set.
Define the set of natural numbers
The set of positive whole numbers, excluding zero
Define the set of integers
The set of whole numbers, including zero and negative whole numbers
Define the set of rational numbers
All fractional numbers.
A number is a member of this set if it can be written as p/q where p and q are integers where q does not equal 0.
Define the set of real numbers
Any number that can be given a decimal representation
Define the set of complex numbers
The set of numbers of the form a + bi where a and b are real and i^2 = -1.
What is the empty set?
A set with no elements
Subset definition
Suppose X is a set. A set Y is a subset of X if every element of Y is an element of X.
What is the definition of a proper subset?
A subset Y of X is called a proper subset of X if Y is not equal to X
Union definition
Suppose that X and Y are two sets. The union of X and Y is the set consisting of all the elements in X or in Y (or in both).
Intersection definition
Suppose that X and Y are two sets. The intersection of X and Y is the set consisting of the elements that are in X and in Y.
When are two sets disjoint?
When their intersection is equal to the empty set
Difference between two sets definition
The set of elements that are in X but not in Y
What is the complement of a set?
The difference between two sets when one of the sets is a subset of the other
What is a power set?
If X is a subset, the power set of X is the set of all subsets of X.
The number of elements is 2^n where n is the number of elements of X.
