We have considered the following problem :
On the identification correspondence between the natural number and the rational number, how becomes the correspondense between the sum of natural numbers and the sum of rational numbers.
And the answer was this :
To the relation of the sum of natural numbers corresponds the relation of the sum of rational numbers.
This means that the addition of the rational number is an extension of the addition of the natural number.
Now, let's consider the case of the multiplication.
Does a similar conlusion hold ?
Here is a triplet of natural numbers that form a relation of the product.
In this case the identification between natural numbers and rational numbers is as follows.
On the other hand, (2 x 3)/1 = 2/1 x 3/1. Thus, to the product of 2 and 3 corresponds the product of rational numbers which correspond to 2 and 3, respectively.
This shows that the multiplication of the rational number is an extension of the multiplication of the natural number.
