1 00:00:00,700 –> 00:00:02,049 Hello and welcome

2 00:00:02,249 –> 00:00:05,704 The mathematical symbol of today is simply an arrow.

3 00:00:06,243 –> 00:00:09,099 More precisely i want to talk about two arrows.

4 00:00:09,114 –> 00:00:11,049 This one and that one.

5 00:00:11,957 –> 00:00:15,657 In mathematics both arrows are used when we talk about maps.

6 00:00:15,786 –> 00:00:18,071 For example lets consider a map f.

7 00:00:19,143 –> 00:00:24,611 Then the first arrow is used, when we want talk about the sets, where the map lives on.

8 00:00:25,086 –> 00:00:29,340 So we have a set X on the left hand side, which we call the domain of f.

9 00:00:29,540 –> 00:00:33,470 and a set Y on the right hand side, which we call the codomain of f.

10 00:00:34,386 –> 00:00:38,928 In other words f maps elements from X into the set Y.

11 00:00:39,814 –> 00:00:44,820 and in order to describe this mapping on the element level, we use the second arrow.

12 00:00:45,714 –> 00:00:48,789 Hence an element on the left hand side, lower case x

13 00:00:48,989 –> 00:00:53,122 is mapped to an element on the right hand side in Y, we call f(x).

14 00:00:54,014 –> 00:00:56,502 In fact this is all you should learn here.

15 00:00:56,702 –> 00:01:00,193 We have two different arrows for the two different levels.

16 00:01:00,929 –> 00:01:02,902 Now maybe lets do a simple example.

17 00:01:03,102 –> 00:01:07,171 So we consider the quadratic function defined on the real number line.

18 00:01:08,186 –> 00:01:13,214 Hence you would use the first arrow to denote that R is mapped into R.

19 00:01:13,957 –> 00:01:19,542 and then you see, we use the second arrow to denote that x is mapped to x squared.

20 00:01:20,529 –> 00:01:24,487 In summary with this the whole function is described.

21 00:01:25,057 –> 00:01:28,216 In the first line we have the domain and the codomain.

22 00:01:28,416 –> 00:01:31,621 and in the second line we see how this assignment should work.

23 00:01:32,457 –> 00:01:36,868 Now if you want to learn more about maps. I have a lot of videos about them.

24 00:01:37,700 –> 00:01:41,323 and with this, i hope i see you next time. Bye!

Q1: When someone says that we have a map $f: A \rightarrow B$, what are $A$ and $B$?

A1: They are sets.

A2: They are real numbers.

A3: They are complex numbers.

A4: $A$ is an element of the set $B$

Q2: If someone says that we have a map $f$ with $2 \mapsto 4$, what does it mean?

A1: It means that $f(2) = 4$.

A2: It means that $f(4) = 2$.

A3: It means that $f$ is defined for all real numbers.