The collection of all ordered n-tuples that can be formed so that they contain one element of the first set, one element of the
second,..., and one element of the n-th set. This collection can be seen as constituting an n-dimensional space in which each
n-tuple designates a cell. The simplest Cartesian product of two sets is a two-dimensional table or a cross-tabulation whose
cells may be used to enter frequencies, to designate possibilities or impossibilities, or to chart the
transitions comprising the behavior of a system.  For more information:   Cartesian Product

The equi-join is performed when certain values contained in one table are matched with values contained within a second (or multiple) table(s).  Use equi-join to join two tables, a source and joining table, that have values from one or more columns in common. One or more columns from each table are compared in the WHERE clause for equal values. For rows in the source table that have a match in the joining table, the data for the source table rows and matching joining table rows are included in the result set. Rows in the source table without matches in the joining table are excluded from the joined result set.The equi-join works great when we want to match corresponding data between multiple tables. But what if there was a need to display data according to their characteristic of inequality? For example, the boss requires a list of all operating systems (os) and their corresponding order id numbers where the order pid is greater than the product pid. The solution? The aptly named non-equi join. For more information, click any one of teh two links below.
 equi-join  equi-join

Of all the types of Theta-join, equi-join is the only one that yields a result in which the compared columns are redundant
     to each other - different names but same values
     The natural-join behaves in exactly the same way as the equi-join but one of the redundant columns (simple or
     composite) is omitted from the result
     Relational join is the principal algebraic counterpart of queries the involve the existential quantifier 'exists'

 Natural Join

For an example of Natural join, click here:     Example of Natural join