Some Periodic Functions

Let’s start with a basic “calculus fact”. Theorem 1  If f is a non-constant, continuous periodic function on R, then there exists a smallest positive real number λ satisfying f(x+λ)=f(x) for all x. Proof: By definition of periodicity, there exists a subset Λ⊂R satisfying f(x+λ)=f(x) for every x∈R and λ∈Λ. Necessarily Λ is closed under …

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