Representation of set

There are usually three ways to represent a collection. Enumeration is a method of enumerating the elements of a collection one by one. For example, the three primary colors in optics can be represented by the set {red, green and blue}; The set A consisting of four letters A, B, C and D can be expressed as a = {a, B, C, d}, and so on.

Enumeration also includes the case that although the elements in the collection cannot be enumerated one by one, their changing rules can be expressed. For example, a positive integer set and an integer set can be represented as and, respectively. {Represents the element | the nature of satisfaction}

Let the set S consist of all elements with a certain property p, then the set can be expressed by describing the common properties of the elements in the set: S = {x | P(x)}

For example, the set b consisting of the square root of 2 can be expressed as B={x|x2=2}.

Rational number set and positive real number set can be expressed as sum respectively. N: non-negative integer set or natural number set {0, 1, 2, 3, …}

N* or N+: positive integer set {1, 2,3, …}

Z: integer set {…,-1, 0, 1, …}

Q: Rational number set

Q+: Set of Positive Rational Numbers

Q-: set of negative rational numbers

R: set of real numbers (including rational numbers and irrational numbers)

R+: positive real number set

R-: negative real number set

C: complex set

: empty set (a set without any elements is called an empty set, also called an empty set)