MindMap Gallery High School Mathematics-Collection Mind Map
This is an article about high school mathematics-set mind map. A collection of elements is called a set, and each object in the set is called an element of the set.
Edited at 2023-11-25 10:22:02This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
The meaning and representation of sets
meaning
A collection of elements is called a set. Each object in a collection is called an element of the collection.
Representation of elements and sets
element
Lowercase letters a, b, c...
gather
Capital letters A, B, C...
relationship with elements
Belongs to
Does not belong to ∉
display method
enumeration method
List the elements of the set one by one
descriptive method
Use certain conditions to indicate whether certain objects belong to this set
Venn diagram
Represented by the area enclosed by a closed curve on the plane
Element properties
certainty
Mutuality
disorder
Classification
finite set
A set with a finite number of elements
infinite set
A collection with infinite elements
empty set
A collection containing no elements
basic relationship
Complete works
If the set contains all elements involved in the problem under study, then the set is called the universal set U.
Subset
If x∈B exists for every x∈A, then A⊆B (or B ⊇ A)
True subset
If the set A⊆B, but there are elements x∈B and x∉A, then
Sets are equal
A⊆B
B⊆A
A=B
empty set
A set without any elements (∅)
subset of any set
Commonly used number sets and symbols
Set of positive integers (N* or N )
Set of integers (Z)
Set of rational numbers (Q)
Set of non-negative integers (set of natural numbers) (N)
Set of real numbers (R)
Basic operations
union
definition
A∪B={x丨x∈A or x∈B}
nature
A∪A=A
A∪∅=A
A∪B=B∪A
intersection
definition
A∩B={x丨x∈A and x∈B}
nature
A∩A=A
A∩∅=∅
A∩B=B∩A
Complement
definition
nature
algorithm
If operations are required between sets, the intersection and complement can help; when a common element group intersects, all elements form a union; if the complement of set A is required, the complete set can be obtained by removing A; the distributive law and associative law are applicable to set operations!
Operation rules
commutative law
A∪B=B∪A
A∩B=B∩A
associative law
(A∪B)∪C=A∪(B∪C)
(A∩B)∩C=A∩(B∩C)
distributive law
(A∪B)∩C=(A∩C)∪(B∩C)
(A∩B)∪C=(A∪C)∩(B∪C)
Morgan's Law
Intersect and Convert
Inclusion-exclusion principle
A∪B = A B - A∩B
A∪B∪C = A B C - A∩B - B∩C - C∩A A∩B∩C
Expand and improve
A collection of n elements
Subset
True subset
non-empty subset
non-empty proper subset
important relationship
A∩B⊆A⊆(A∪B)
A∩B=A↔A⊆B
A∪B=B↔A⊆B
Problem solving ideas
Combining Numbers and Shapes Thoughts
Classify discussion ideas
complement thought
Misunderstanding warning
When finding the value or range of letters in a set, the mutuality of elements should be verified, otherwise multiple solutions are likely to occur.
0∈N, but 0∉N*
A⊆B, we need to consider whether A=∅ is true
A∩B=∅, consider A=∅ or B=∅
∅⊆ {0}