Between two Real Numbers exists Rational Number/Proof 1/Historical Note

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Historical Note on Proof 1 of Between two Real Numbers exists Rational Number

When this proof was first published in 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces, there was a mistake in it:


This was corrected in the second printing, along with an apologetic note:

Preface to reprinted edition
I am grateful to all who have pointed out errors in the first printing
(even to those who mentioned that the proof of Corollary 1.1.7
purported to establish the existence of a positive rational number
between any two real numbers). In particular ...