I'm reading through this proof that any homogeneous equation can be rewritten as . It says that, by homogeneity, for all real (I think it should have the proviso that , but it doesn't.). It then claims--and here's the part I don't get--that an appropriate choice of may be . I thought was some real number, not a real-valued function. Am I missing something important here, or should I just take homogeneity to mean something like for any function ?