A2. Peter wrote down the set of all numbers that are greater than twice the value of their squares in the form of an interval. What did he write?
(A) $(0,1)$
(B) $[0,1]$
(C) $\left(0, \frac{1}{2}\right)$
(D) $\left(\frac{1}{2}, 2\right)$
(E) $\left[\frac{1}{2}, 1\right]$
A2. Let's write the inequality $x>2 \cdot x^{2}$. We rearrange and factor the inequality to get $x(1-2 x)>0$. We read off the zeros $x_{1}=0$ and $x_{2}=\frac{1}{2}$. On the number line, we mark the signs and determine that the solution is the interval $\left(0, \frac{1}{2}\right)$.