Why is $P(X=2.5)=0?$ The discrete random variable X has cdf 
$$\left\{
  \begin{array}{rcr}
    0   & = & \text{for} \ x<1 \\
    1/4 & = & \text{for} \ 1\le x<2 \\
    3/4 & = & \text{for} \ 2\le x<3 \\
    1   & = & \text{for} \ x\ge 3
  \end{array}
\right.$$
Find a) $P(X=1)$, b) $P(X=2)$, c) $P(X=2.5)$, d) $P(x\leq2.5).$
I found a), b) and d) easy by drawing out the peacewise cdf. I fail to se why $P(X=2.5)=0$. If $2.5\in 2\le x<3,$ shouldn't the answer be the same as in b), that is $\frac{3}{4}-\frac{1}{4} = \frac{1}{2}?$

It might help to express this as a probability mass function.
$$P_X(x)=\left\{
  \begin{array}{rcr}
    1/4  & x=1 \\
    2/4  & x=2 \\
    1/4  & x=3 \\
    0 & \text{otherwise}
  \end{array}
\right.$$
