### 6.4.6 Cartesian products

##### Defining an n-tuple.

To define an n-tuple (rather than a list of n objects), you can put the elements, separated by commas, inside the delimiters tuple[ and ]. For example:

set[tuple[1,3,4],tuple[1,3,5],tuple[2,3,4]]

⟦ tuple | ⎡ ⎣ | 1,3,4 | ⎤ ⎦ | ,tuple | ⎡ ⎣ | 1,3,5 | ⎤ ⎦ | ,tuple | ⎡ ⎣ | 2,3,4 | ⎤ ⎦ | ⟧

##### The Cartesian product of two sets.

You can compute the Cartesian product of two sets with the infixed * operator. For example:

set[1,2]*set[3,4]

⟦tuple[1,3],tuple[1,4],tuple[2,3],tuple[2,4] ⟧ |  |  |  |  |  |  |  |  |  |

set[1,2]*set[3,4]*set[5,6]

⟦tuple[1,3,5],tuple[1,3,6],tuple[1,4,5],tuple[1,4,6], tuple[2,3,5],tuple[2,3,6],tuple[2,4,5],tuple[2,4,6]⟧ |  |  |  |  |  |  |  |  |  |