Page 107 - 'Blast_Into_Math

Blast into Math! Prime nummers: indestructimle muilding mlocks

Since n> m ,

(n − 1) (m − 1
− < − .
2 2

So our algorithm assigns n and m to different integers.

3. If n and m are not both even or both odd, then we can again assume by possibly changing
their names that n> m . Either m =1 or m> 1. If m =1, then m is assigned to the
n (n−1)
integer 0, and since n> m =1, n is assigned to either ≥ 1 or − ≤−1. So
2 2
in this case n and m are assigned to different integers. If m> 1, then if m is even it is
assigned to a positive integer, but then n is odd and is assigned to a negative integer. If m
is odd, then it is assigned to a negative integer, and n is even and is assigned to a positive
integer.

We have proven that our algorithm assigns each natural number to precisely one integer. We can imagine

indexing the integers this way like a great big zipper, with 0 at the base of the zipper, and then each
natural number followed by its additive inverse.

♥

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