MATH 412 ADVANCED CALCULUS HOMEWORK #2
Due September 12, 2007
1. Show that set {1,10,100,··· ,1 0 ·· ·0
| {z }
k−1}has kelements.
2. Suppose that Ais a set with melements, Bis a set with nelements, and set A∪B
has kelements. Show that if k < m +n, then Aand Bare not disjoint.
3. If Ais a set with melements (m≥2) and B⊆Ais a set with 2 elements, show that
A\Bis a set with m−2 elements.
4. Find a bijection between the sets Eand O, where Eis the set of all even natural
numbers and Ois the set of all odd natural numbers.
5. Show that set {13,23,33,···n3,· ··} is denumerable.
6. Prove that set {1,6
√2,··· ,6
√n, ··· } is denumerable.
7. Suppose that set Ais denumerable, Bis a set with 2 elements. Show that if Aand B
are disjoint, then set A∪Bis also denumerable.
1