Hints and Solutions

  • Antonio Caminha Muniz Neto
Part of the Problem Books in Mathematics book series (PBM)


If there exists a bijection f : I1 → I n , show that n = 1. Now, assume that m,n > 1 and there exists a bijection f : I m  → I n . Letting k = f(m), show that there exists a bijection g : I n  ∖{k}→ In−1, so that \(g\circ f_{|I_{m-1}}:I_{m-1}\rightarrow I_{n-1}\) is also a bijection. Then, use an inductive argument to deduce that m − 1 = n − 1.


  1. 8.
    A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)Google Scholar
  2. 9.
    A. Caminha, An Excursion Through Elementary Mathematics II - Euclidean Geometry (Springer, New York, 2018)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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