Cartesian product


THEOREM   

The Cartesian product is not commutative.

$$A \times B \ne B \times A$$

Proof available

THEOREM   

The Cartesian product is not associative.

$$A \times B \times C \ne A \times (B \times C)$$

Proof available

LEMMA    \(A \times \emptyset = \emptyset\)

Proof unavailable

LEMMA    \(\emptyset \times A = \emptyset\)

Proof unavailable

THEOREM    Cartesian product of countable sets is countable.

Proof available

See also

Parent topics