Convergent Sequence Space4 Discuss the set of all convergent sequences as a vector space,...

Convergent Sequence Space4 Discuss the set of all convergent sequences as a vector space, where the addition of “vectors” and multiplication by a scalar are defined by

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Describe the zero element and additive inverse elements for this vector space. Make a conjecture about the dimension of and try to back it up. Give at least one example of a non-trivial subspace and discuss its dimension.