Fundamentals of Mathematics-Basic definitions (sets, set of real numbers, mappings, functions)

This series of articles only provides a workable solution for quick review after learning the notes for the basic Records of mathematics definition Collection:Refers to a collective of specific or abstract objects of a particular nature, which are called elements of the collection. Base:The number of elements in the collection is called the cardinality of the collection, also known as the potential (recorded as | a|）

Common set: natural number: N \mathbb{n} integer: Z \mathbb{z} rational Number: Q \mathbb{q} real: R \mathbb{r} plural: C \mathbb{c} empty set: ∅\varnothing

indicates that the symbol exists: ∃\exists any: ∀\forall *

set Operation intersection: A∩b=x:x∈a and x∈b a \cap b= {x:x \in A and X\in B} set: A∪b=x:x∈a or x∈b a \cup b= {x:x\in A or x \in B} difference set: A∖b=x:x∈ A and x∉b a \setminus B = {X:x\in A and X\notin B}

interval opening interval: (A, b) = {x:a<x<b x:a} closed interval: [A, b] = {x:a≤x≤b x:a \leq x \leq B}

field Area: U (A,ϵ) u (A, \epsilon) = {x:a−ϵ<x<a+ϵx:a-\epsilon} hollow field: U0 (A,ϵ) u_0 (A, \epsilon) = {x:a−ϵ< X<a+ϵ and X≠a x:a-\epsilon}

set of real numbers

Point one by one on the number and the axes on the set of real numbers Rational number : In a dense way on the axis: ∀ (A, B) ∩q≠∅\forall (A, b) \cap \mathbb{q } \neq \varnothing

Z≈n \mathbb{z} \approx \mathbb{n}
N≈