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

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Homework Help Overview

The discussion revolves around the notation and meaning of F[a][b] and F[a,b] in the context of polynomial sets. Participants are exploring the differences between these two forms and their implications in algebra.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the definitions and relationships between F[a][b] and F[a,b]. Questions are raised about the nature of these sets and their respective elements.

Discussion Status

Some participants have provided insights into the definitions of F[a][b] and F[a,b], noting their isomorphic relationship. However, there remains a level of confusion regarding the notation and its implications, indicating ongoing exploration of the topic.

Contextual Notes

There is mention of a textbook that introduces F[a][b] without sufficient explanation, contributing to the participants' confusion about the notation.

futurebird
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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?
 
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futurebird said:
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!
 


Hurkyl said:
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? :-p
 


futurebird said:
Great! But what the heck are they? :-p
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
 


Hurkyl said:
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!

:rolleyes:
 

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