Question: 1. "It doesn't matter if you want infinitely many cookies, you can still send a few our way!"
How is it possible for one person to have infinitely many cookies and still send some down?
2. "LA3: The operations researcher made a list of all possible groups of lab assistants, right? And every group has to meet about someone's primary project. The operations researcher came up with every possible group, and one of those is the group of lab assistants who are not in the group that discusses their primary project. And apparently there's no project for that group to discuss. "LAB ASSISTANT: Let's pretend that this particular group is going to discuss my primary project every lab assistant in this group is not in the group that discusses his or her primary project. So I can't be in the group. And that means I am not in the group that discusses my primary project, which means I am in the special group, which is discussing my primary project. It just goes 'round and 'round."
(a) LA3 and Lab Assistant's dialogue suggests a function from the set of groups of lab assistants to the set of projects. What is that function? Describe/define it verbally and using function-and-set-theoretic notation.
(b) In turn, this suggests a function from the set of groups of lab assistants to the set of lab assistants. What is that function? (Please call it f)
(c) Consider the group of lab assistants who are not in the group that discusses their primary project. Define this group g using set-theoretic notation.
(d) What is f(g)?
(e) Is f(g) ∈ g? Explain.
(f) Explain why there cannot be a bijection between the set of groups of lab assistants and the set of lab assistants.
(g) What is the relationship between the groups of lab assistants and the lab assistants themselves?
(h) What cardinality conclusion does this present?