Find an explicit bijection (i.e. give a formula that explains what f(x) is given any x ∈ [0, 1]) between [0, 1] and [0, 1).
Question
Find an explicit bijection (i.e. give a formula that explains what f(x) is given any x ∈ [0, 1]) between [0, 1] and [0, 1).
Solution
Sure, here is a simple bijection between [0, 1] and [0, 1):
f(x) =
- 1/2 if x = 1
- x otherwise
This function is a bijection because it is both injective and surjective. It is injective because no two different inputs will give the same output. It is surjective because every element in the range [0, 1) is the image of some element in the domain [0, 1].
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