Axler Linear Algebra:: What does this notation mean?

[Saladsamurai]

In chapter 1 of Axler's LA Done Right, he defines a polynomial as such:

"Our next example of a vector space involves polynomials. A function p:\mathbf{F}\rightarrow\mathbf{F} is called a polynomial with coefficients in
F ..."

Can someone translate this "p:\mathbf{F}\rightarrow\mathbf{F}" into words? I have never seen that notation before.

[nicksauce]

"p: A->B" means p is a function with domain A and codomain B. Or in other words, p takes elements from the set A and outputs members of the set B.

[Saladsamurai]

Thanks! How would one know that btw? That is, what subject does one learn that in?

[HallsofIvy]

Normally, one learns what "F:A-> B" means in basic algebra or pre-calculus.

[g_edgar]

Thanks! How would one know that btw? That is, what subject does one learn that in?

Normally, one uses textbooks in conjunction with an instructor, and the instructor answers such questions. I guess this board is a (slow) substitute for having an instructor...

[Saladsamurai]

Normally, one uses textbooks in conjunction with an instructor, and the instructor answers such questions. I guess this board is a (slow) substitute for having an instructor...

Yeah. That's the route I am going. My maths seem to be lacking when it comes to the fundamentals. I have completed all of the math in my engineering requirement and have performed very well, but a lot of the base details seem to be missing. Not sure why. But I am reteaching myself all of the math I have learned (and more) from a more 'pure' perspective.

As a result, PF will have to deal with the onslaught of stupid questions that I usually harass my teachers with :redface:

GO PF!!