Let V consist of the form ^→ u = (u1, u2, ..., un, ...) in which

u1, u2, ..., un, ... is an infinite sequence of real numbers. Define two infinite sequences to be equal if their corresponding components are equal, and define addition and scalar multiplication componentwisebyo

⃗u ⃗v = (u1, u2, ..., un, ...) + (v1, v2, ..., vn, ...) =(u1 +v1,u2 +v2,...,un +vn,...)

k⃗u = (ku1, ku2, ..., kun, ...). Prove that the given set is a vector space

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Hence V is closed under vector addition Hen... View the full answer