Conditional Probability Notation random variable vs number

Question

I am confused by the notation for the definition of a martingale.

$E(X_{n+1}/X_n,....,X_1) = X_n$

I understand that $X_n$ here refers to the realized value but I don't understand why it is written as a capital $X_n$ and not as $x_n$. For example $E(Y/X)$ refers to a random variable and $E(Y/X=x)$ refers to a number.

Answer 1

We don't know what the values of $ X_{n+1}$ and $X_n$ will be, but on average, once we know $X_n$, we expect $X_{n+1}$ to worth around $X_n$.