Question

Prove that the inverse of an isometry is again an isometry. (This implies that the set of isometries is closed under the inverse operation.)

   Prove that the inverse of an isometry is again an isometry. (This implies that the set of isometries is closed under the inverse operation.)

Exploring Geometry

Exploring Geometry

Michael Hvidsten 2nd Edition

Chapter 5, Problem 2

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Step 1

An isometry is a function \( f: X \to Y \) between metric spaces \( (X, d_X) \) and \( (Y, d_Y) \) such that for all \( x, x' \in X \), the distance between \( f(x) \) and \( f(x') \) in \( Y \) is the same as the distance between \( x \) and \( x' \) in \( X \). Show more…

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Prove that the inverse of an isometry is again an isometry. (This implies that the set of isometries is closed under the inverse operation.)

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