• Title: Empty Set

  • Series: Advent of Mathematical Symbols

  • YouTube-Title: Empty Set

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  • Subtitle on GitHub: aoms26_sub_eng.srt

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  • 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

    16 00:01:17,343 –> 00:01:23,018 and if you want to learn more details, I have a whole course about this called “start learning sets”.

    17 00:01:23,443 –> 00:01:27,954 So I hope that I meet you there or in the next video about mathematical symbols.

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  • Last update: 2024-11

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