# Question: let be the set of infinite sequences with coordinatewise addition...

###### Question details

let be the set of infinite sequences with coordinatewise addition and multiplication.

Determine (prove or give a reason) which of the following subsets of are subspaces

(a) the set of sequences with only finitely many

(b) the set of sequences with only finitely many

(c) (K=R)The set of sequences such that

(d)(K=R)The set of sequences such that

(e)(K=R)The set of sequences such that