I'm viewing a basic series of youtube videos on sets. This slide has me all kinds of confused.
His example starts with a set X. The elements of this set are denoted as $A_k \subset X$. He then takes the $\cup_i^{inf}\cap_j^{inf}A_j$. He lists k as an index in the natural numbers {1,2,3...inf}.
His demonstration shows what I believe to be an infinite series of subsets, ${A_1,A_2,A_3,A_4,...}$.
His example starts with two subsets $A_{odd},A_{even}$ and proceeds do demonstrate how to take the union/intersection of the 2 different sets.
How am I supposed to derive that $A_3$ exists? Is this setup so that X is just the infinite alternating series of subsets equal to X = {$A_{odd},A_{even},A_{odd},A_{even},A_{odd},A_{even}, ... $}?
It appears to me that the set X only has two sets, {$A_{even}, A_{odd}$}, so how does it make sense to reference an $A_j$ that is equal to 3?