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Recall that the following identification between natural numbers and rational numbers holds by taking the point of view of "equivalence of multipliers"
Here let's consider a triplet of natural numbers that form a relation of the sum.
In this case the identification between natural numbers and rational numbers is as follows.
On the other hand, (2 + 3)/1 = 2/1 + 3/1. Thus, to the sum of 2 and 3 corresponds the sum of rational numbers which correspond to 2 and 3, respectively
This shows that the addition of the rational number is an extension of the addition of the natural number.