Let T ⊆ R {\displaystyle {}T\subseteq \mathbb {R} } be a subset and let
be a continuous function. Let x ∈ T {\displaystyle {}x\in T} be a point such that f ( x ) > 0 {\displaystyle {}f(x)>0} . Prove that f ( y ) > 0 {\displaystyle {}f(y)>0}