Social Security number function

[srfriggen]

Homework Statement

For the given relation, indicate if it is surjective, injective, both (bijective), or neither, and give a brief rationale for your answer.

"The function that assigns to everybody in the US their social security number."

The Attempt at a Solution

The wording on this, to me, isn't too clear, but my guess is that it means the Domain is possible Social Security numbers, and the Codomain is "everybody in the US." If you interpret it differently, please let me know.

Not everybody in the US has a social security number, so it certainly is not surjective. It is injective, since each SS# is assigned to one and only one person.

However, the thing that is throwing me off is, is it a function if there are elements in the domain that are not assigned to any element in the codomain? For example, the SS# 000-00-000 has never been used, so I'm not sure if that matters.

So it is either "neither", since it is not a function, or "injective".

 

[jbunniii]

"The function that assigns to everybody in the US their social security number."

The wording on this, to me, isn't too clear, but my guess is that it means the Domain is possible Social Security numbers, and the Codomain is "everybody in the US." If you interpret it differently, please let me know.

I interpret it to mean the other way around: the domain is "everybody in the US" and the codomain is "social security numbers." Unfortunately, this is ill-defined because not everybody in the US has a social security number. A function MUST assign a value to every element in the domain. If this were assigned to me, I would assume (and write a sentence indicating my assumption) that the domain should be "everybody in the US who has a social security number."

 

[jedishrfu]

There are several documented instances where the same SS# was given more than one person:

http://www.cbsnews.com/news/for-20-million-americans-one-social-security-numbers-not-enough/

 

[srfriggen]

cool, thanks!