A function f:A→B from set A to set B is called a bijection
if it is a one-to-one correspondence between A and B, i.e. for every b in B there is exactly one a in A such that f(a)=b. More informally, you could say that every element in A gets matched up with exactly one element in B and vice versa.
Can you give examples for bijections between the following sets?
1. A=(0,1), B=R
2. A=[0,1]², B=the unit disc with boundary, i.e. all points in the plane with distance smaller or equal 1 from origin
3. A=[0,1], B=the unit circle, i.e. all points in the plane with distance 1 from the origin.
4. A=[0,1], B=the unit disc with boundary
(In reply to part 3
Many of these would have solutions if only one end were inclusive rather than both ends.
Posted by Charlie
on 2006-09-21 15:25:05