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### Proof help for the existence of a function in Velleman 3rd Chapter 8 section 2

Think of listing the possible triples $(a, b, c)$ in order (it's a countable set). Now sequentially choose an $n(a, b, c)$ for each and define $f(a \cdot n(a, b, c)+b) = c$. You need to make sure that ...
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### Compressing the primes using simple addition?

Here's what I've found. I was concentrating more on keeping $\sup(A+B)$ fairly small than on maximising $|A+B|$. \begin{array}{rrllrr} |A|&|B|&A&B&\sup(A+B)&|A+B|\\ 5&5& 5, ...
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