1 thought on “(01. UN DULODUN U Morg)<br />Suppose f and g are two functions with respective domains X and Y, then g is called an<br />extension”
You have certainly dealt with functions before, primarily in calculus, where you studied functions from R to R or from R2 to R. Perhaps you have encountered functions in a more abstract setting as well; this is our focus. In the last few sections of the chapter, we use functions to study some interesting topics in set theory.
By a function from a set A to a set B we mean an assignment or rule f such that for every a∈A there is a unique b∈B such that f(a)=b. The set A is called the domain of f and the set B is called the codomain. We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a).
Step-by-step explanation:
You are familiar with many functions f:R→R: Polynomial functions, trigonometric functions, exponential functions, and so on. Often you have dealt with functions with codomain R whose domain is some subset of R. For example, f(x)=x−−√ has domain [0,∞) and f(x)=1/x has domain {x∈R:x≠0}. It is easy to see that a subset of the plane is the graph of a function f:R→R if and only if every vertical line intersects it at exactly one point. If this point is (a,b), then f(a)=b. □
You have certainly dealt with functions before, primarily in calculus, where you studied functions from R to R or from R2 to R. Perhaps you have encountered functions in a more abstract setting as well; this is our focus. In the last few sections of the chapter, we use functions to study some interesting topics in set theory.
By a function from a set A to a set B we mean an assignment or rule f such that for every a∈A there is a unique b∈B such that f(a)=b. The set A is called the domain of f and the set B is called the codomain. We say two functions f and g are equal if they have the same domain and the same codomain, and if for every a in the domain, f(a)=g(a).
Step-by-step explanation:
You are familiar with many functions f:R→R: Polynomial functions, trigonometric functions, exponential functions, and so on. Often you have dealt with functions with codomain R whose domain is some subset of R. For example, f(x)=x−−√ has domain [0,∞) and f(x)=1/x has domain {x∈R:x≠0}. It is easy to see that a subset of the plane is the graph of a function f:R→R if and only if every vertical line intersects it at exactly one point. If this point is (a,b), then f(a)=b. □