In this paper, we develop theoretical foundations for relational (table) databases. Two mathematical formalisms such as table algebra of infinite tables and multiset table algebra are considered. The question of the relationship between table algebra of infinite tables and multiset table algebra is also considered. As the main result, we show the equivalence of table algebra of infinite tables and corresponding relational calculi. This result generalises the classical result about the equivalence of Codd’s relational algebra and tuple (domain) relation calculus.