1 and q are rational number sets, but q does not represent rational numbers. Rational number set and rational number are two different concepts. The set of rational numbers is the set of all rational numbers, and rational numbers are all elements in the set of rational numbers. Rational number is the collective name of integer (positive integer, 0, negative integer) and fraction, and it is the set of integer and fraction.

2. The origin of rational number naming

The name "rational number" is puzzling, and rational numbers are no more "reasonable" than other numbers. In fact, this seems to be a mistake in translation. 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.