2 - Products of sets and indexed sets

Cartesian Products

The cardinality of a Cartesian product of two sets can be found by multiplying them together. The cartesian product is a set!

If you find the Cartesian product of a set with itself, it can be written $A^2$ instead of A x A

The Cartesian plane is ${\mathbb{R}}^2$ or $\{(x,y):x,y\in R\}.$

The Cartesian product of a set with the empty set will always be the empty set and have a Cardinality of 0.

You can form a set with ordered triples:

Ordered lists are lists of things where order matters. For example, an ordered pair

1. A, C, D
2. A, D
3. D, G

a) -{-1, 1, -9 , 9}
b) {}
c) All the squares and their negatives
d) All the squares and their negatives
e) {}
.

HW 2

![[H2_submission.pdf]]