
Title: Map Arrows

Series: Advent of Mathematical Symbols

YouTubeTitle: Advent of Mathematical Symbols  Part 16  Map Arrows

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Timestamps

Subtitle in English
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!