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Math Amateur

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I am currently focused on Chapter 2: Relations, Functions and Orderings; and, in particular on Section 3: Functions

I need some help with H&J's depiction of invertible functions and their relationship to one-to-one functions ...H&J's section on invertible and one-to-one functions (including examples) reads as follows:View attachment 7588

View attachment 7589In the above text from Karel Hrbacek and Thomas Jech (H&J) we read the following:" ... ... 3.8 Theorem. A function is invertible if and only if it is one-to-one ... ... "Surely it is better if we define things so a function is invertible if and only it is a bijection ... and this, I think ist the usual approach ...

Why do MHB members think H&J define things this way ... what are the benefits of defining invertible functions the way H&J do ...

Any comments ... would like to know what readers think ... should I persevere with H&J as a text ...Peter