# Discrete Math: Matching Zeros

Two Social Security numbers match zeros if a digit of one number is zero if the corresponding digit of the other is also zero. In other words, the zeros in the two numbers appear in exactly the same positions. For example, the Social Security numbers 120-90-1109 and 430-20-5402 have matching zeros.

Prove: Given a collection of 513 Social Security numbers, there must be two that match zeros.

25.16: Let f: N -> Z by

f(n) = set of -n/2 if n is even and (n+1)/2 if n is odd.

Prove that f is bijection.

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#### Solution Preview

Please see attached.

24.14

a) f(x)=2x is one to one but not onto because f(x) = 3 has no solution, because that would make 2x=3 which is impossible.

b) f(x) = 10+x is both one to one and onto

c) f(x) = 10+x is not onto in this case. Because f(x) = 5, would be 10+x=5, which makes x=-5. Not possible because f:N->N.

d) f(x) is one to one and onto.

25.9

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#### Solution Summary

The expert finds a bijection between two data sets.