This isn't entirely accurate. SS numbers were created specifically with the intent of not being an identification, and were labeled as such. They were created

This isn't entirely accurate. SS numbers were created specifically with the intent of not being an identification, and were labeled as such. They were created to track people in the Social Security program. Since you can't be dead and enrolled in SS, they don't need to be unique. Duplicates have also been issued in the past by accident. The SS Administration (man, that sounds really bad) claims it has issued 450 million SSN's since the beginning of the program (which is interesting considering there's 322 million people in the US today) and that it has space for "several generations" without re-issuing numbers or increasing the number of digits. Although the number space is 9 digits, the structure of the records allows for far less than 1 billion real SSNs. The numbers have existed since 1936, and have been required for every US citizen since 1990. With 5.5 million new SSNs issued every year, it could take around 120 years to run out of numbers at the current rate.