# What is function

#### Amer

##### Active member
I want to teach it what is a function can you give me your definition and an example, thanks

#### Fantini

MHB Math Helper
Given two sets $X$ and $Y$, a function is a rule assigning each element in $X$ one element in $Y$, which we denote $f: X \to Y$. Note that all elements of $X$ must be associated to elements of $Y$, but not necessarily all of $Y$.

#### Amer

##### Active member
I make an example which is the human it is an function between the time and the place it is impossible to a human to be in two places in the same time and in every time human located in a place

#### Fantini

MHB Math Helper
Yes, it looks okay. It's a bit strange worded, but perhaps this is what you meant: you have a function which, given any time, returns a person's location at that given time. Since at one time an individual cannot be at two places, it is a function.

Cheers.

#### HallsofIvy

##### Well-known member
MHB Math Helper
A function, from set X to set Y, is a set of ordered pairs, first member an element of X, second member an element of Y, such that two pairs cannot have the same first member but different second members.

An example would be with X the set of students in your class, Y numbers. The set of ordered pairs would be a student and the student's weight. Two students might have the same weight but a single student would not have two different weights.

This is, of course, the same Fantini's definition with his rule telling how the pairs are formed, my pairs defining his rule.