V-4-is-a-set-of-all-real-valued-continues-functions-defined-on-the-entire-real-line-together-with-standard-addition-and-scalar-multiplication-Is-V-4-a-vector-space-Explain-

Question Number 167519 by MikeH last updated on 18/Mar/22

$$\mathcal{V}_{\mathrm{4}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{real}\:\mathrm{valued}\:\mathrm{continues}\: \\ $$$$\mathrm{functions}\:\mathrm{defined}\:\mathrm{on}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{real} \\ $$$$\mathrm{line}\:\mathrm{together}\:\mathrm{with}\:\mathrm{standard}\:\mathrm{addition} \\ $$$$\mathrm{and}\:\mathrm{scalar}\:\mathrm{multiplication}.\:\mathrm{Is}\:\mathcal{V}_{\mathrm{4}} \: \\ $$$$\mathrm{a}\:\mathrm{vector}\:\mathrm{space}?\:\mathrm{Explain} \\ $$

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