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


  • Set

    An un­ordered col­lec­tion of dis­tinct ob­jects.