• Title: Element Symbol

  • Series: Advent of Mathematical Symbols

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

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  • Subtitle on GitHub: aoms25_sub_eng.srt

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  • 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

    18 00:01:36,457 –> 00:01:42,993 and if you want to learn more about this I have a whole video course about this called “start learning sets”.

    19 00:01:43,193 –> 00:01:47,977 So let’s meet there or on the next day for the next mathematical symbol.

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