2. Enumeration: A description method of a collection, in which the elements in the collection are enumerated one by one and enclosed in curly braces. Note: Elements need to be separated by ",". Elements are non-repetitive and unordered. If there are many elements and there are obvious rules, the ellipsis can be omitted.
3. Description: The set is represented by the same characteristics of the elements in the * * * set. The specific method is: write the general symbols and range of values representing the elements of this set with curly braces, then draw a vertical line and write the general characteristics of the elements after the vertical line. The general form is {x∈I|P(x)}, where x is the representative form of elements in the set, I is the range of x, and P(x) is the * * * isomorphism of elements.
Enumeration method is suitable for cases where there are no * * * common features between elements, description method is suitable for cases where there are * * * common features between elements, and natural language method is suitable for cases that cannot be described above.
Extended data
Set, for short, is a basic concept in mathematics and the main research object of set theory. The basic theory of set theory was founded in19th century, and the simplest statement about set is the definition in naive set theory (the most primitive set theory).
That is, a set is a "definite pile of things", and the "things" in the set are called elements. A modern set is usually defined as a whole consisting of one or more definite elements.
fuzzy set
Sets used to express fuzzy concepts are also called fuzzy sets and fuzzy subsets. A public collection refers to the sum of objects with certain attributes. The concept expressed by this attribute should be clear and well defined.
Therefore, the subordinate relationship between each object and the set is also clear, either one or the other. But there are still many vague concepts in people's minds, such as young, old, warm, late and so on. The object attributes described by these concepts cannot be simply answered with "yes" or "no", but a fuzzy set refers to all objects with attributes described by a fuzzy concept.
Because the concept itself is not clear, the definition is not clear, so the subordinate relationship between object and set is not clear, either one or the other. This concept was first put forward in 1965 by L.A. Zadeh, a cybernetic expert at the University of California.
The emergence of the concept of fuzzy set enables mathematical ideas and methods to deal with fuzzy phenomena, thus forming the basis of fuzzy set theory (commonly known as fuzzy mathematics in China)? .
Equal set
If the elements of two sets S and T are exactly the same, then the two sets S and T are said to be equal and marked as S = T ... Obviously, there is the following relationship:
Turn left | turn right
Wherein the symbol
Turn left | turn right
Called if and only if, it means that the proposition on the left and the proposition on the right contain each other, that is, the two propositions are equivalent.
Symbolic method
Some sets can be represented by some special symbols, such as:
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)
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