Question

Social Security numbers contain nine digits. Suppose that all nine-digit numbers are allowable Social Security numbers. Is there a one-to-one correspondence between allowable Social Security numbers and U.S. residents? You may assume that the U.S. population is about 300 million. Explain your answer.

Answer 1

The answer to the question is;

No, one-to-one correspondence between allowable Social Security numbers and U.S. residents will be in place only when the allowable digits equal the population size.

Explanation:

Where there are nine-digit social security numbers then there are a total of 1 to 999999999 or Nine hundred and ninety nine million, nine hundred and ninety nine thousand, nine hundred and ninety nine hundred possible social security numbers

Since the U.S. population is 300 million, then there is not a one to one correspondence as all the 999,999,999 different digits are allowable to the given 300,000,000 population. That is there are jumped numbers between the social securities numbers of the 300 million U.s. population.