Thanks for the response, it is a very clear proof via Taylor's theorem. I am still wondering though if it is possible to prove from the definition provided. The problem is that Taylor's theorem is introduced after this particular definition and theorem. I definitely appreciate the proof via...
Thanks for the feedback, I changed the latex tags to use ## which seems to have produced the desired effect.
I actually just finished looking through every analysis book in my schools science library (rudin, funke, hille, haeussler, etc...) over 30 books and not one of them had this particular...
Homework Statement
In the book "Friendly introduction to analysis, 2nd Ed." by kosmala there is a definition of the root of a function and subsequent theorem and proof. Either the proof is not directly addressing certain important properties, or is flawed. The definition and theorem are as...