Difficult)))
I do not understand the switching back and forth between an indeterminate and a variable of a function...
I do not understnd the significance or value in corollary 4.19 and why its useful that a function that maps on infinite fields is the same iff it is induced by the same polynomial?? what would make this so useful?
Seems almost trivial to try to apply the number of roots to a possibly infinite degree polynomial...??
Reflective)))
Polynomial functions are what we operate in for calculus and differential equations! I feel so at home here working on fields of polynomials and polynomial functions defined for every polynomial in the field. The usefullness of roots and factors, and irreducible polynomials not having roots is almost like a little safety zone for me to retreat to for a few days after struggling with the idea of X being indeterminate...but to let it be a variable that describes a rule of the function...I really feel like the stantard needs to be changed and the distinction made MORE CLEAR on when X is a variable and when it is a determinate.
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