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Can you match them up? (Posted on 2006-09-21) Difficulty: 5 of 5
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], 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

No Solution Yet Submitted by JLo    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: part 3 | Comment 3 of 6 |
(In reply to part 3 by bumble)

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
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