-1

Consider set $W = \{ W_e | e \in \mathbb{N}\}$, where the $W_e$'s are sets of natural numbers. define set $K = \{e | e \in W_e\}$. Obviously K is some type of "diagonal" set. I'm confused abut its definition, as the symbol "$e$" appears as both an element of $W_e$ and its subscript.

Can someone please clarify this? I appreciate all help, am

Kevin Long
  • 5,159
Agapito Martinez
  • 53
  • Additionally, it is claimed that the complement of K cannot be identical to any of the W_e's. Can someone please indicate why this should be the case? Thanks again. Agapito – Agapito Martinez Oct 10 '17 at 19:24

1 Answers1

0

Each $W_e$ is a set of natural numbers. These sets are indexed by natural numbers as well. I could have $W_0=\varnothing, W_1=\{3,4,5\}, W_2$ be the set of even numbers, etc. In this case, $0\notin W_0, 1\notin W_1, 2\in W_2$, so $2\in K$, and $0,1\notin K$.

Kevin Long
  • 5,159