Concept explainers
The base for a recursive definition of a set is _____
To fill:
The base for a recursive definition of a set is ______.
Answer to Problem 1TY
The base for a recursive definition of a set is a statement that certain objects belong to the set.
Explanation of Solution
Given information:
a recursive definition of a set
Calculation:
To define a set of objects recursively, you identify a few core objects as belonging to the set and give rules showing how to build new set elements from old. More formally, a recursive definition for a set consists of the following three components:
I. BASE: A statement that certain objects belong to the set.
II. RECURSION: A collection of rules indicating how to form new set objects from those already known to be in the set.
III. RESTRICTION: A statement that no objects belong to the set other than those coming from I and II.
Thus, the base for a recursive definition of a set is a statement that certain objects belong to the set.
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