Recent content by dhong

Hey PF! Can you help me with something: Players alternately choose 0's or 1's. A play of this infinite game is thus a sequence of 0's and 1's. Such a sequence can be considered as the binary expansion of a real number between 0 and 1. Given a set ##E## of real numbers satisfying ##0 < x < 1...

Homework Statement Suppose the function ##f:[0,1] \to \mathbb{R}## is continuous, ##f(0) > 0## and ##f(1)=0##. Prove that there is a number ## x_0 \in (0,1] : f(x_0) = 0## and ##f(x) > 0## for ##0 \leq x \leq x_0##. Homework Equations We can't use the IVT. Additionally, the definition of...