Set product

define the product as tuples

several examples, including R^n being the product over \(\{1,2, \dots, n\}\); this introduces associativity of the product which is covered later

product is associative up to isomorphism, though not literally

cardinality of the product, noting that in the finite case it collapses to just the usual definition of the product of natural numbers

as an aside, define the product formally in ZF

link to universal property, mentioning it is a product in the category of sets