Define a set S recursively as follows:I. BASE: 1 ? S, 2 ?

Chapter 5, Problem 8E

(choose chapter or problem)

Problem 8E

Define a set S recursively as follows:

I. BASE: 1 ∈ S, 2 ∈ S, 3 ∈ S, 4 ∈ S, 5 ∈ S, 6 ∈ S, 7 ∈ S, 8 ∈ S, 9 ∈ S

II. RECURSION: If s ∈ S and t ∈ S, then

a. s0 ∈ S b. st ∈ S

III. RESTRICTION: Nothing is in S other than objects defined in I and II above.

Use structural induction to prove that no string in S represents an integer with a leading zero.