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## Homework Statement

Let [itex] n_1=min(n\in\mathbb{N}:f(n){\in}A) [/itex]

As a start to a defintion of g:N→A, set [itex]g(1)=f(n_1) [/itex]

Show how to inductively continue this process to produce a 1-1 function g from

N onto A.

## The Attempt at a Solution

[itex] g(1)=f(n_1) [/itex] so this is our base case for induction.

so [itex] g(2)=f(n_1+1) [/itex]

If I understand this correctly g is a function that has input values of natural numbers and maps these to the set A.

So I guess I need to show that f(n) is in A and f(n+1) is in A

By definition f(n) is in A for all n, so f(n+1) is in A for all n.

Could I maybe do a proof by contradiction and assume that f(n+1) was not in A and show that it was because n+1 is in the Naturals, therefore it works for f(n), and f(n+1)

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