What you’ll learn
Understand sequences as functions.
Key idea
A function can have a discrete domain; it need not be defined for every real number.
Repeated terms and undefined noninteger indices do not violate functionhood on the specified domain.
Worked example
Classify examples and non-examples for the concept 'Understand sequences as functions'.
Sequence -2,-5,-8,... follows the explicitly stated arithmetic continuation with difference -3, for n=1,2,3,... Classify n→a_n as a function with domain evidence.
- The stated arithmetic continuation has difference -3; index n maps to the unique output a_n=-3n+1.
- Only positive integer indices belong to this sequence domain. Repeated outputs or a changing term value do not violate output uniqueness per index.
Answer: Function — every positive integer index is assigned one term by the stated rule.
Quick Check
Classify examples and non-examples for the concept 'Understand sequences as functions'.
Sequence -5,-5,-5,... follows the explicitly stated arithmetic continuation with difference 0, for n=1,2,3,... Classify n→a_n as a function with domain evidence.