Power Set, Theory of Linear Algebra, and Axiomatic Systems

69 Views Asked by At

So for homework, my History of Math professor gave us these three questions:

  1. Explain why the power set of a set S (collection of all subsets) has the same cardinality as the set [all functions from S to the codomain {0,1}].
  2. What is the key role of (some special kinds of) functions to the theory of Linear Algebra?
  3. What is the modern view of an "axiomatic system"? (How was this influenced by Non-Euclidean Geometry?)

We have not learned anything related to this and I could not find any of this information in my textbook.