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

$${\mathcal{V}}_4\mathrm{is}\mathrm{a}\mathrm{set}\mathrm{of}\mathrm{all}\mathrm{real}\mathrm{valued}\mathrm{continues}$$$$\mathrm{functions}\mathrm{defined}\mathrm{on}\mathrm{the}\mathrm{entire}\mathrm{real}$$$$\mathrm{line}\mathrm{together}\mathrm{with}\mathrm{standard}\mathrm{addition}$$$$\mathrm{and}\mathrm{scalar}\mathrm{multiplication}.\mathrm{Is}{\mathcal{V}}_4$$$$\mathrm{a}\mathrm{vector}\mathrm{space}?\mathrm{Explain}$$

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