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).
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Solution 1

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 ra Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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