Help understanding a paragraph in Kadane's book Principles of uncertainty

Question

Consider two infinite sequences of indicators of events, $s_1$ and $s_2$, with respective relative frequencies $l_1$ and $l_2$, where $l_1\neq l_2$. Let $A$ be the indicator of an event not an element of $s_1$ or $s_2$. Consider new sequences $s^\prime_1 = (A, s_1 )$ and $s^\prime_2 = (A, s_2 )$. These sequences have relative frequencies $l_1$ and $l_2$, respectively. Hence within this theory the event A does not have a well-defined probability.

Quote is from page 76/77.

I am confused in how to understand $s_i$. What does it mean that $A$ is not an element of $s_1$ or $s_2$?

It also says

...Let $A$ be the indicator of an event not an element of $s_1$ or $s_2$.

What does this mean? $s_i$ are supposed to be sequences of of indicators, not events. So how do the new sequences look like, namely $s^\prime_i$? Also, why do they have the same relative frequencies $l_i$.

Answer 1

There is usually some equation in the book relating to these variables: s,l,A can you add that information for clarity?

I believe that A not being an element of $s_i$ means that if you were to create a ven diagram A would not fall into the category of event indicators enclosed by $s_i$

$s^′_i$ seems to just be a notation that it was produced with the pair of event indicators $s_i\ and\ A$ and not to be confused with $s_i$ or it could be a derivation, if an equation is provided it could help clarify this for me.