Unformatted text preview: f : [0 , 1] → (0 , 1). Problem 2. (*) Show that if X and Y are two sets, and both f : X → Y and g : Y → X are injective, then there exists a bijective map h : X → Y . This is really quite tricky; think of going from X to Y to X . . . and forming chains as long as you can. How do these chains begin and end? To how many chains can an element of X or Y belong? Finally, in Section 2.1.3, do exercises 1, 3, 4, 6, 7. These are easy as compared to the previous ones....
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- Fall '07
- Math, bijective map, explicit bijective map