# Thread: List the elements of S produced by the first five applications of the recursive defin

1. ## List the elements of S produced by the first five applications of the recursive defin

Let S be the subset of the set of ordered pairs of integers
defined recursively by

Basis step: (0, 0) ∈ S.

Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S
and (a + 3, b + 2) ∈ S.

a) List the elements of S produced by the first five applications
of the recursive definition.

How do I know which (a,b) pairs to use? I know that it's the first five but I don't know how to get the first five.

2. ## Re: List the elements of S produced by the first five applications of the recursive d

the recursion step forms two new pairs. So, at each step you could also form (a + 3, b + 2) from (a, b), not necessarily (a + 2, b + 3). In fact, the process of generating new pairs branches at each step and the order in which pairs are generated is not determined.

3. ## Re: List the elements of S produced by the first five applications of the recursive d

Originally Posted by lamentofking
Let S be the subset of the set of ordered pairs of integers
defined recursively by Basis step: (0, 0) ∈ S.
Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S
and (a + 3, b + 2) ∈ S.
a) List the elements of S produced by the first five applications of the recursive definition.
$\displaystyle \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}$

I am somewhat confused as to exactly the phrase "the first five applications of the recursive definition" actually means.
You may need to either drop the (0,0) or make 4 a 5 in the above.

BTW LaTeX seems to be down: \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}

4. ## Re: List the elements of S produced by the first five applications of the recursive d

Originally Posted by Plato
$\displaystyle \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}$

I am somewhat confused as to exactly the phrase "the first five applications of the recursive definition" actually means.
You may need to either drop the (0,0) or make 4 a 5 in the above.

BTW LaTeX seems to be down: \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}
first five applications are the first five definitions.