TITLE: Suppose that $x$ is a fixed nonnegative real number such that for all positive real numbers $E$ , $0\leq x\leq E$. Show that $x=0$.
QUESTION [5 upvotes]: Suppose that x is a fixed nonnegative real number such that for all positive real numbers $E$ , $0\leq x\leq E$. Show that $x=0$.

REPLY [4 votes]: If $x>0$, then $0<\frac{x}{2}<x$.

REPLY [2 votes]: Assume towards contradiction that $x>0$. Then $\frac{x}{2}$ is a positive real number. How does this contradict your assumption?