ℕ is the standard symbol for set natural (counting) numbers. Set of natural numbers is defined as {1, 2, 3, ...}. The ellipsis "..." means it's infinitely countable or the numbers goes on forever.
Definition: The cardinality of a set is a measure of a set's size, meaning the number of elements in the set. So if you have set A = {2, 3, 4, 6}, Therefore the cardinality of set A, with a symbol |A| or n(A), is equal to 4.
|A| = 4 or n(A)=4
Therefore the cardinality of ℕ, which is |ℕ|, is infinity.
|ℕ| = ∞ or n(ℕ) = ∞
Definition: The standard symbol for integers is Ζ (Zahlen symbol) and is defined also as {...-3, -2, -1, 0, 1, 2, 3,...}. Therefore, the set {m∈Z m is even Λ m ≤ -100} is the set {...,-102, -101, -100} and it is also infinitely countable no matter if you are counting from left to right or right to left. The symbol Λ can be read as the word "and" or "intersect with". Furthermore, the symbol ∈ can be read as "is an element of".
| {m∈Z m is even Λ m ≤ -100} | = ∞.
Therefore
ℕ and {m∈Z m is even Λ m ≤ -100} has the same cardinality and they are both equal to infinity (∞).
