Sets of number.
N = the set of natural numbers {0, 1,2,3,….}
Z = the set of integers {…,-2,-1,0,1,2,….}
Z+ = the set of positive integers {1,2,3,….}
Q = the set of rational numbers {p/q
| p ∈ Z,q ∈ Z, and q = 0}
R = the set of real numbers {
R+ = the set of
positive real numbers
C = the set of complex numbers.
Set equality.
Definition =
Two sets are equal if and only if they have the same
elements. Therefore, if A and B are sets,
then A and B are equal if and only if ∀x(x ∈ A ↔ x ∈ B).We write A = B if A and B are
equal sets.
Example =
The sets {4, 5, 6} and {6, 4, 1} are equal, because they
have the same elements. The
order in which the elements of a set are listed does not
matter. {1, 3, 3, 3, 5, 5, 5, 5} is the same as the
set {1, 3, 5} because
they have the same elements. Eventhough element of a set is listed more than
once ,it does not matter.
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