Sets of number & Set equality

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.