(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Decide which of the following are subrings of the ring of all functions from the closed interval [0,1] to R (the reals)

a) The set of all functions f(x) such that f(q) = 0 for all q in Q (the rationals) & q in [0, 1]

b) The set of all polynomial functions

c) The set of all functions which have only a finite number of zeros, together with the zero function

d) The set of all functions which have an infinite number of zeros.

e) The set of all functions f such that lim {x -> 1+} f(x) = 0

f) The set of all rational linear combinations of the functions sin(nx) and cos(mx) where m and n are non-negative integers

2. Relevant equations

3. The attempt at a solution

The first one is pretty straight forward to show that it is a subring. But unless I'm mistaken, the sets mentioned from b to f aren't even subsets let alone subgroups or subrings since they can be defined on a larger domain than [0,1]. Am I correct? Or am I reading it wrong?

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# Homework Help: Doing a problem on rings from Dummit & Foote I think I'm mis-reading it

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