F[a][b] vs F[a,b]: What's the Difference?

[futurebird]

What is F[a]?

I'm having a hard time with notation. If F[x] is the set of polynomials in x, then what is:

F[a]?

How is it different from F[a,b]?


And help would be great?

 

[Hurkyl]

I'm having a hard time with notation. If F[x] is the set of polynomials in x, then what is:

F[a]?

How is it different from F[a,b]? And help would be great?

The very pleasant thing is that F[a,b] really is isomorphic to F[a], just like we want it to be!

 

[futurebird]

The very pleasant thing is that F[a,b] really is isomorphic to F[a], just like we want it to be!

Great! But what the heck are they?

 

[Hurkyl]

Great! But what the heck are they?

F[a] is the set of polynomials in b whose coefficients are elements of F[a]
F[a,b] is the set of bivariate polynomials in a and b whose coefficients are elements of F

 

[futurebird]

F[a] is the set of polynomials in b whose coefficients are elements of F[a]

Oh that makes sense-- it's sort of recursive... OK. God my book is so muddled and just starts talking about F[a] out of the blue like it's clear what that would mean.

Thank you so much no I can keep studying!