I know that a set (let's call it V) of all functions which map (R -> R) is a vector space under the usual multiplication and addition of real numbers, but i am having trouble proving it, i understand that the zero vector is f(x)=0, do i just have to prove that each element of V remains in V under additon and scalar multiplication? If that's the case then i cant work out how to go about proving it, if it isnt the case, then what exactly am i proving?(adsbygoogle = window.adsbygoogle || []).push({});

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# Proving a set to be a vector space,

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