This is a translation error. The word rational number comes from the west and is rational in English. Rational usually means "rational". China translated western scientific works in modern times into "rational numbers" according to Japanese translation methods. However, this word comes from ancient Greece, and its English root is ratio, which means ratio (the root here is English and the Greek meaning is the same). So the meaning of this word is also very clear, that is, the "ratio" of integers. In contrast, "irrational number" is a number that cannot be accurately expressed as the ratio of two integers, but it is not unreasonable.

An important difference between rational number set and integer set in extended data is that rational number set is dense and integer set is dense. After arranging rational numbers in order of size, there must be other rational numbers between any two rational numbers, which is density. Integer sets do not have this feature, so there are no other integers between two adjacent integers.

Rational numbers are compact subsets of real numbers: every real number has a rational number that is arbitrarily close. A related property is that only rational numbers can be transformed into finite continued fractions. Rational numbers have an ordered topology according to their sequences. Rational number is a (dense) subset of real number, so it also has subspace topology.

Resource Rational Number _ Baidu Encyclopedia