Week 3 and 4 - Sets Flashcards
What is a set?
A collection of unique elements where there is no order between the elements.
What needs to be true about an element in order for it to be in a set? (3 things)
Needs to be identifiable
Need to be able to say if the element is in the set or not
Every element needs to be unique
For the set A, what is the set A*?
A set of sequences of elements of A
What is the cardinality of a set?
The number of elements in a set
How can the cardinality of 2 sets be compared without counting the number of elements in each set?
By pairing up elements from each set. Then you can see if the sets are the same size or if one is bigger.
If a set has the same cardinality as the natural numbers then it is called…
Countable or countably infinite
The set of the real numbers are uncountable because…
it has a cardinality greater than the natural numbers
What is a subset?
A set is a subset of another set if all of its elements are also in that set.
An empty set is a…
Subset of every set
What is a powerset of the set A?
A set containing all of the subsets of A
How do you find the cardinality of a powerset?
2 ^ n
