imtheembers replied to your post “imtheembers replied to your post: I CAN’T BELIEVE IT IT’S THE FIRST...”
TF? Was the set {ℕ} defined differently somewhere?
Ah, but that's the thing. You're treating ℕ like it has its own value instead of it representing the natural numbers group. Basically, ℕ={1,2,3,4,...}.
The question was whether 2 was an element of {{1,2,3,4,...}}, and the answer is no. It's like you're taking a family with 4 different members, and then another family with 3 different members, and then make a new set that's called Families. You'll only have two elements in that set, not 7.
Let's call family 1 A. A={1,2,3,4}. Let's call family 2 B. B={5,6,7}. Let's call the family set F. F={A,B}={{1,2,3,4},{5,6,7}}. Set F only has the two elements. That's it. While 1 is an element of A, it is NOT an element of F. You can't dig into the curly brackets. You may not touch the inside of the curly brackets. The inside of the curly brackets have a NO ENTRY road sign on them that glows in the dark. Just because {1,2,3,4} LOOKS like 1,2,3,4 doesn't mean they're the same thing.
... at least, according to my very limited understanding of set theory. figmentsoutoffundamentals, halp. The maths are back.