knowverseQuestion 1
What is the cardinality of the empty set?
The empty set contains no elements.
Source excerpt
When we say the empty set has a cardinality of zero, we are describing its most defining feature.
From the Knowverse course text.
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Membership and size
A set is determined by its elements. Roster notation lists them inside braces, while set-builder notation specifies a rule within a domain. Changing the order of listed elements does not change the set. A clear domain makes it possible to decide which objects are being considered when applying a membership rule.
Cardinality counts the elements of a finite set. The empty set has cardinality zero, but a set containing the number zero has one element. A subset contains only elements of another set. A proper subset also leaves out at least one element of that other set, so the two sets differ.
Source excerpt
The number of elements in a set is called its cardinality.
From the Knowverse course text.
Combining sets and forming pairs
A union contains elements found in either of two sets, including their shared elements only once. An intersection contains just the shared elements. Disjoint sets have no shared elements, so their intersection is empty. Set difference keeps the elements of one set that do not belong to the other.
A power set contains all the subsets of a set, including the empty set and the original set. Ordered pairs introduce a different concern: position matters. A Cartesian product forms pairs by taking the first entry from one set and the second from another. If either set is empty, no such pairs exist.
Source excerpt
This complete set of all possible pairings is called the Cartesian product of the two sets.
From the Knowverse course text.