key term - Set Notation

Definition

Set notation is a way to represent and describe sets, which are collections of distinct objects or elements. It provides a concise and standardized method to define and manipulate sets in mathematics, particularly in the context of topics such as domain and range.

5 Must Know Facts For Your Next Test

1. Set notation uses curly braces $\{\}$ to enclose the elements of a set.
2. The elements within a set are separated by commas, and the set is denoted by a capital letter, such as $A$, $B$, or $S$.
3. The cardinality of a set, denoted as $|A|$, represents the number of elements in the set.
4. The empty set, denoted as $\emptyset$, is a set with no elements.
5. Set operations, such as union, intersection, and complement, can be represented using set notation.

Review Questions

• How can set notation be used to define the domain of a function?
  • The domain of a function is the set of all possible input values for the function. In set notation, the domain can be represented as the set of all $x$ values for which the function is defined. For example, if a function $f(x)$ is defined for all real numbers, the domain can be written as $\{x \in \mathbb{R}\}$, where $\mathbb{R}$ represents the set of real numbers.
• Explain how set notation can be used to describe the range of a function.
  • The range of a function is the set of all possible output values for the function. In set notation, the range can be represented as the set of all $y$ values that the function can produce. For instance, if a function $f(x)$ has a range of all positive real numbers, the range can be written as $\{y \in \mathbb{R}^+\}$, where $\mathbb{R}^+$ represents the set of positive real numbers.
• Analyze how set notation can be used to represent the relationship between the domain and range of a function.
  • The relationship between the domain and range of a function can be expressed using set notation. For example, if a function $f$ maps elements from the domain set $A$ to the range set $B$, this can be denoted as $f: A \rightarrow B$, where $A$ represents the domain and $B$ represents the range. This set notation highlights the correspondence between the input values (domain) and the output values (range) of the function, allowing for a concise and precise representation of the function's behavior.

Related terms

Set: A set is a well-defined collection of distinct objects or elements.

Element: An element is a member or individual item that belongs to a set.

Subset: A subset is a set that is contained within a larger set, where all the elements of the smaller set are also elements of the larger set.