recursive

Examples of recursive in the following topics:

• Recursive Definitions

  • This definition is valid because, for all $n$, the recursion eventually reaches the base case of $0$.
  • Depending on how the sequence is being used, either the recursive definition or the non-recursive one might be more useful.
  • A geometric sequence follows the formula $a_n=r\cdot a_{n-1}.$ This is another example of a recursive formula.
  • Using this equation, the recursive equation for this geometric sequence is: $a_n=2 \cdot a_{n-1}.$
  • Use a recursive formula to find specific terms of a sequence

• Introduction to Human Language

  • Human language is unique because it is generative, recursive, and has displacement.
  • Specifically, human language is unique on the planet because it has the qualities of generativity, recursion, and displacement.
  • Human language is recursive.
  • Obviously, the recursive abilities of language are constrained by the limits of time and memory.
  • Human language is also modality-independent—that is, it is possible to use the features of displacement, generativity, and recursion across multiple modes.

• Introduction to Practical Procedures

  • To recursively elaborate previously learned procedural and cultural mathematical competencies, each emphases section will have the 5th emphasis on the Practical Procedures of this level of mathematics.

• Sequences

  • Sequences whose elements are related to the previous elements in a straightforward way are often specified using recursion.
  • To specify a sequence by recursion requires a rule to construct each consecutive element in terms of the ones before it.
  • The Fibonacci sequence can be defined using a recursive rule along with two initial elements.

• Introduction to Sequences

  • These are called recursive sequences.
  • The recursive definition is therefore $a_n=a_{n-1}+3, a_1=10.$
  • The recursive definition is therefore $a_n=a_{n-1}-3, a_1=25$.
  • Therefore the recursive definition is $a_n=3a_{n-1}, a_1=2$.
  • Therefore the recursive formula is $a_n=\frac13\cdot a_{n-1}, a_1=162$.

• Blending Content with Pedagogy

  • Recursively elaborate mathematics.

• Describing Qualitative Data

  • Alternatives to coding include recursive abstraction and mechanical techniques.
  • Recursive abstraction involves the summarizing of datasets.

• Speed of Innovation

  • Phases can be iterative and recursive (meaning that they do not proceed linearly from one to the next; rather, earlier phases can be returned to for further improvement as needed).

• Types of Innovation

  • Phases can be iterative and recursive (meaning that they do not proceed linearly from one to the next; rather, earlier phases can be returned to for further improvement as needed).

• Geometric Sequences

  • Such a geometric sequence also follows the recursive relation $a_n=ra_{n-1}$ for every integer $n\ge 1.$