This set is the only set whose power set is a singleton. For 10 points each:
[10e] Name this unique set that contains no elements. This set can be denoted with a circle with a slash through it.
ANSWER: empty set [or null set]
[10m] For finite set X with cardinality n, this expression gives the number of elements in the power set of X because determining each element in the power set involves deciding between inclusion and exclusion of each element in X.
ANSWER: two to the power of n [or nth power of two]
[10h] This statement suggests that there are no sets with cardinality between that of the natural numbers and their power set. Paul Cohen developed forcing to show that this statement cannot be proven from the ZFC axioms.
ANSWER: continuum hypothesis [or CH]
<Yingzhi Nyang, Science - Math> ~20696~ <Editor: David Bass>