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

Suppose that x is a fixed nonnegative real number such that for all positive real numbers $E$ , $0\leq x\leq E$. Show that $x=0$.

score 4 · Answer 1 · answered Mar 05 '13 at 14:02

4

If $x>0$, then $0<\frac{x}{2}<x$.

answered Mar 05 '13 at 14:02

score 2 · Answer 2 · answered Mar 05 '13 at 14:02

2

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

answered Mar 05 '13 at 14:02

T. Eskin

2 Answers2