“A function is invertible if the function and its inverse relation are both bijections.“
We found the above written as a definition for “invertible” and then we got scared.
(our rewrite) “A function is invertible if it is a bijection.”
Appendix A
An element of a set is invertible if the set contains an inverse for that element
Appendix B
As written, everything idea contained in the first definition is true. However, if a function is a bijection, it is guaranteed that the inverse function is also a bijection.
Wouldn’t it be better to shorten one definition of “invertible” and make the word “bijection” do more of the work?
Rob Sterling 