Understanding Elements of Sets in Set Theory 📚

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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