Mathematical Language and Symbols

Flashcards on Mathematical Language and Symbols based on lecture notes.

Mathematical Language

A unique language that provides precise expression for every thought or concept.

Set

Any group or collection of objects.

Elements/Members

The objects that belong in a set.

Rule Method

Describing the property of a given set.

Roster Method

Listing the elements of the set, enclosing them by braces, and separating each of them by a comma.

Set-Builder Notation

Introducing a variable to represent an arbitrary element of the set and describing this variable such that the description fits to all elements of the set.

Finite set

A set with a last element or a set that has a fixed number of elements

Infinite set

A set with no last element

Unit set

A finite set with only one element

Null/Empty set

A set that contains no element (void)

Universal set/Universe

A set that contains all the elements in the discussion or investigation

Complement of a Set

The set of all elements of the universal set U that are not elements of A

Subset of B

If every element in a set A is also a member of a set B

Proper Subset

Every element of A is an element of B, and A ≠ B

Union of Sets

The set that contains all the elements that belong to A or to B or to both.

Intersection of Sets

The set of elements common to both A and B.

Difference of Sets

The set that contains the elements of A but not the element of B.

Cartesian Product

The set of all ordered pairs (a,b) such that a is an element of A and b is an element of B.

Relation

Any set of ordered pairs.

Domain of the Relation

The set of first components of the ordered pair

Range of the Relation

The set of all second components

Function

A relation in which each member of the domain corresponds to exactly one member of range

Function

A correspondence between a first set, called domain, and a second set, called the range, such that each element in the domain corresponds to exactly one element in range.

Statement

A declarative sentence that is either true or false, but not both true and false.

Simple Statement

A statement that conveys a single idea.

Compound Statement

A statement that conveys two or more ideas.

Tilde Symbol

Denotes the negation of a statement.