# Modular arithmetic question about functions

 P: 366 Yes, it does make sense. Have you studied abstract algebra yet? Modular arithmetic is a special case of quotient objects, in this case a quotient ring. On Wikipedia they have some good examples involving polynomials and smooth functions. For another example, let $R := \{f \in C[0,1] : f \quad \text{is continuous} \}$ be the ring of continuous real-valued functions defined on [0,1]. Given $f \in R$ we can define an equivalence relation by g~h iff $g(x) - h(x) =a(x)f(x)$ for some function $a(x) \in R$. Another way to write this would be g(x) = h(x) mod (f(x))