Question

Give a recursive definition of a) the set of odd positive integers

a) Recursive Odd Integers
b) Odd Integer Set Formula
c) Positive Odd Numbers
d) Recursion for Odd Integers

Answer 1

The recursive definition of the set of odd positive integers starts with 1 as the base case and defines that if n is an odd positive integer, n + 2 is also an odd positive integer, thereby generating all odd positive numbers in the sequence 1, 3, 5, 7, etc. The correct option is c) Positive Odd Numbers

Step-by-step explanation:

The recursive definition of the set of odd positive integers can be given as follows:

1. Base case: 1 is the smallest odd positive integer.
2. Recursive step: If n is an odd positive integer, then n + 2 is also an odd positive integer.

This recursive definition starts with the number 1, which is the first odd positive integer, and then generates subsequent odd integers by repeatedly adding 2. The recursive process will continue indefinitely, producing all the odd positive integers in the set: 1, 3, 5, 7, ...

Using this definition, we can generate odd positive integers in a sequence where each number is two more than the previous, starting with 1. For example, starting with 1 and applying the recursive step, we get 1, 1+2=3, 3+2=5, and so on.

The correct option is c) Positive Odd Numbers