• Title: Element Symbol

• YouTube-Title: Advent of Mathematical Symbols - Part 25 - Element Symbol

• Bright video: https://youtu.be/jOgZWYaF8jc

• Dark video: https://youtu.be/6CLX6vQipd0

• Subtitle on GitHub: aoms25_sub_eng.srt

• Timestamps (n/a)
• Subtitle in English

1 00:00:00,714 –> 00:00:03,814 Hello and welcome back to the next mathematical symbol.

2 00:00:03,857 –> 00:00:06,431 Which is today the element symbol.

3 00:00:06,971 –> 00:00:11,793 This is exactly written like this. So you take a lower case c with a line inside it

4 00:00:12,414 –> 00:00:18,131 and then you use it as a binary operator, where we have a left-hand side and the right-hand side.

5 00:00:18,786 –> 00:00:24,982 On the right-hand side you find a given set and on the left-hand side an element of this set.

6 00:00:25,182 –> 00:00:29,790 So you would read it like: " a is in A"

7 00:00:30,400 –> 00:00:35,398 and now you remember, this is the sole operation we need to describe sets.

8 00:00:36,014 –> 00:00:41,750 Hence the visualization would be that the set A is such a collection of elements.

9 00:00:42,457 –> 00:00:49,262 This means if “a in A” is a true statement, we would draw the lower case a inside the capital A.

10 00:00:49,743 –> 00:00:56,787 However it’s also possible that the set A is also an element in another larger set.

11 00:00:57,457 –> 00:01:03,113 So we could write capital A is an element of a larger set curved A.

12 00:01:03,829 –> 00:01:08,550 Hence for this it would mean, the visualization is exactly the same.

13 00:01:08,914 –> 00:01:13,363 So capital A can be seen as a point in this curved A.

14 00:01:13,563 –> 00:01:18,121 So we learn, such an object can be an element, but also a set.

15 00:01:18,200 –> 00:01:21,249 So it can be on the right-hand side, but also on the left-hand side.

16 00:01:21,449 –> 00:01:28,297 So in the visualization it would mean, if you zoom in, you see that this element has also elements for itself.

17 00:01:29,286 –> 00:01:36,060 So there we have it. This is the element symbol we use throughout mathematics to describe the element-set relation