Understanding Elements of Sets in Set Theory ๐
Learn what elements are in sets, how they define the set, and explore key concepts like cardinality and set membership in this comprehensive guide.

Wrath of Math
53.9K views โข Jan 26, 2019

About this video
What are elements of sets? Recall that a set is an unordered collection of distinct objects. The elements of a set are the distinct objects that the set contains.
For example, consider the set S = { 1, 2, 3 }. In this case, the numbers 1, 2, and 3 are the elements of S. While a number like 4 is not an element of S.
Elements of sets can be anything, for example, the set A = { 4, { 1, 3 }, red } contains the number 4, the set { 1, 3 }, and the color red. It is important to notice that A does not contain 1 and A does not contain 3; but A does contain the set that contains 1 and 3. This distinction can be very tricky at times.
Recall S = { 1, 2, 3 }. How many elements are in the set S? There are 3 elements in S. We call the number of elements in a set the cardinality of the set. So the cardinality of S is 3, and we write this as |S| = 3. You might recognize we use the absolute value bars, which are more generally used to indicate a measure of magnitude, like the cardinality of a set.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
โ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons
Follow Wrath of Math on...
โ Instagram: https://www.instagram.com/wrathofmathedu
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For example, consider the set S = { 1, 2, 3 }. In this case, the numbers 1, 2, and 3 are the elements of S. While a number like 4 is not an element of S.
Elements of sets can be anything, for example, the set A = { 4, { 1, 3 }, red } contains the number 4, the set { 1, 3 }, and the color red. It is important to notice that A does not contain 1 and A does not contain 3; but A does contain the set that contains 1 and 3. This distinction can be very tricky at times.
Recall S = { 1, 2, 3 }. How many elements are in the set S? There are 3 elements in S. We call the number of elements in a set the cardinality of the set. So the cardinality of S is 3, and we write this as |S| = 3. You might recognize we use the absolute value bars, which are more generally used to indicate a measure of magnitude, like the cardinality of a set.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
โ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons
Follow Wrath of Math on...
โ Instagram: https://www.instagram.com/wrathofmathedu
โ Facebook: https://www.facebook.com/WrathofMath
โ Twitter: https://twitter.com/wrathofmathedu
My Music Channel: http://www.youtube.com/seanemusic
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Video Information
Views
53.9K
Likes
846
Duration
4:20
Published
Jan 26, 2019
User Reviews
4.7
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