Reviewing notes 2.1 of Mathematical analysis

Chapter2 Numerical sequence and function

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Cartesian product set

If S and T are sets,then the cartesian product set S×T is formed by taking all ordered pairs (p,q) where p∈S and q∈T.

Relations,functions

Any subject f of the cartesian product S×T is called a relation between S and T. A relation f is called a function if for every p∈S such that (p,q)∈f.This element q is denoted by f(p).The set S is the domain of f and the set T is the codomain of f. A function f from a set S into E¹ is a real valued function. If for every q∈T there is some p∈S such that q=f(p), then we say f is onto T. If for any a,b∈S,a≠b implies that f(a)≠f(b), then we say f is univalent.

Numerical sequence

A numerical sequence is a special type of real function that its domain is N₊,denoted as {Xn}.Therefore we have Xn=f(n),n∈N₊.