Let \((x_n)_{n\in\mathbb N}\) and \((y_n)_{n\in\mathbb N}\) be two rational Cauchy sequences. The multiplication of rational Cauchy Sequences can be defined based on the multiplication of rational numbers as follows: \[\begin{array}{cclc} (x_n)_{n\in\mathbb N}\cdot (y_n)_{n\in\mathbb N}&:=&(x_n\cdot y_n)_{n\in\mathbb N}\\ \end{array}\] i.e. the product of two rational Cauchy sequences is a new rational sequence, whose sequence members are the products of rational numbers being the corresponding members of the original two rational Cauchy sequences.
Moreover, the new rational sequence \((x_n\cdot y_n)_{n\in\mathbb N}\) is also a rational Cauchy sequence.
Proofs: 1
Proofs: 1 2 3 4 5 6 7 8 9
Propositions: 10 11 12 13 14 15
