Confused about Continuous Random variable Hello I have just begun learning about continuous random variables, and I am already confused on the first example given.
I know that the probability distribution function of a random variable X, is given by $$F(x)=P(X \le x)$$ $$x \in \mathbb{R}$$
The example given is,
Suppose that X is the number that results when we roll an unfair die that has probabilities $P(x=1)=.2$
$P(x=2)=.1 $
$P(x=3)=.2 $
$P(x=4)=.1 $
$P(x=5)=.2$ 
$P(x=6)=.2$
Then find the probability distribution function.
It then gives the solution]
$F(x)= 0$ if $-\infty \lt x \lt 1$ 
$=.2$ if $1 \le x \lt 2$
$=.3$ if $2 \le x \lt 3$
$= .5$ if $3 \le x \lt 4$
$=.6$ if $4 \le x \lt 5$
$=.8$ if  $5 \le x \lt 6$
$=1$ if $6 \le x \lt \infty$
But this is so confusing to me. I mean I of course see what is happening, in that they are adding the probabilities.
But lets take for example $F(x)=.5$ if $3 \le x \lt 4$
How is this .5? isnt the probability that X is less than 4 and greater or equal to 3 just the probability that x is 3? What is the .5?
and isnt the probability that x is greater than or equal to 2 , but less than 3 just equal to the probability that x is 2?
I am really confused, hopefully someone understands what I am trying to ask.
Thanks

For $3\le x<4$, using that $X$ takes its values on $\{1,2,3,4,5,6\}$ (almost surely), we have
$$F(x)=P(X<x)=P(X\le 3)=P(X=1)+P(X=2)+P(X=3)\,.$$
