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Dimensional analysis is the process of obtaining results by analysing the units and dimensions in questions, equations, and so on using The Principle of Homogeneity. Note: DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.
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Is it possible to prove that units can be manipulated algebraically?
I suppose that the best way to argue for this is to consider the units as indicative of the vector space from which the quantities in question originate. The algebra that we have defined in physics is …