In other words, when something different is considered as a whole, the whole is called a set.
The individuals contained in the collection are called elements.
Determinism here means that elements can only be included or not included in the set, and there is no ambiguous state.
Relevance means that the elements in the set are different,
Disorder means that the arrangement of elements in a set does not affect the similarities and differences of the set.
Disorder means that the arrangement order of elements does not affect the set. The set is still this under different arrangement orders, but it will be affected if it is an ordered array. If there are n elements, it is called an ordered n-tuple.
Mutuality means that the elements in a set are different from each other, but in reality, the same elements will appear and then multiple sets will be introduced, which will be discussed later.
Let set A be set, and the number of elements in set A is recorded as #A, that is, the cardinality of A..
According to the number of sets, sets are divided into finite sets and infinite sets.
An empty set is a set without elements. Now it is generally believed that empty sets are finite sets.
The definition of a finite set means that the elements in the set are finite. More precisely, it is a non-empty set, which is not equivalent to its own proper subset.
The comparison of the number of finite sets is very simple, just compare the numbers directly.
For an infinite set, it can be obtained by the corresponding way of elements.
Such as a set of positive integer and all numbers in that open interval from 0 to 1,
First, a corresponding relationship is established,
From 2 to positive infinity, corresponding to 1/n, n is an integer from 2 to positive infinity, obviously 1/n is in this open interval,
According to the definition of irrational numbers, irrational numbers can't be expressed by fractions, so take an irrational number: half of the root sign corresponds to 1.
Then there are still elements in the open interval that cannot match the elements in the positive integer set, so there are more elements in the open interval (0, 1) than in the positive integer set.
Enumeration is to list the elements one by one with curly braces, such as A={a, b, c},
The description method is to limit all elements to corresponding relationships with some rules, such as b = {x | 1
Set a = {x | 1
Can be expressed as a∈A, b? Answer.