• Title: Empty Set

• YouTube-Title: Advent of Mathematical Symbols - Part 26 - Empty Set

• Bright video: https://youtu.be/CdbGQo-k8QQ

• Dark video: https://youtu.be/bxf8kZ4Mews

• Timestamps
• Subtitle in English

1 00:00:00,429 –> 00:00:03,539 Hello and welcome back to the next mathematical symbol.

2 00:00:03,739 –> 00:00:06,380 Which is today the empty set symbol.

3 00:00:07,114 –> 00:00:12,203 Usually it’s denoted like this, but sometimes you also see just this set brackets

4 00:00:12,700 –> 00:00:18,157 and as the name tells us, both things just denote a set, which is empty.

5 00:00:18,414 –> 00:00:21,327 So it’s a set with no elements at all.

6 00:00:21,527 –> 00:00:28,196 This means the logical statement given by “x is an element of the empty set” is always false

7 00:00:28,396 –> 00:00:34,064 and exactly because of this result, you can formulate some strange statements for the empty set.

8 00:00:34,600 –> 00:00:43,875 So for example you can say: “for all x in the empty set it holds, if x an even number it’s also an odd number”.

9 00:00:44,543 –> 00:00:49,913 So at first glance it looks false, but it’s indeed a true logical statement.

10 00:00:50,243 –> 00:00:54,791 Simply because there are no elements x in the given set here.

11 00:00:54,991 –> 00:00:57,632 Hence it does not matter what we claim here.

12 00:00:58,071 –> 00:01:00,679 In fact this is what can happen in mathematics.

13 00:01:00,879 –> 00:01:08,417 That you prove a very surprising statement, but then it turns out that you have actually proven it just for the empty set

14 00:01:08,771 –> 00:01:12,083 and then the claim does not hold any information at all.

15 00:01:12,743 –> 00:01:17,020 Ok and with this I would say we have learned what the empty set symbol is