# Rational-numbers sentence example

The arithmetic of

**rational numbers**is now established by means of appropriate definitions, which indicate the entities meant by the operations of addition and multiplication.A real number is a class (a, say) of

**rational numbers**which satisfies the condition that it is the same as the class of those rationals each of which precedes at least one member of a.This is exactly the same reason as that which has led mathematicians to work with signed real numbers in preference to real numbers, and with real numbers in preference to

**rational numbers**.The compactness of the series of

**rational numbers**is consistent with quasi-gaps in it - that is, with the possible absence of limits to classes in it.Thus the class of

**rational numbers**whose squares are less than 2 has no upper limit among the**rational numbers**.AdvertisementFurthermore, incommensurable numbers are defined as the limits arrived at as the result of certain procedures with

**rational numbers**.Furthermore, the sort of continuity of the series (in order of magnitude) of

**rational numbers**is known to be different from that of the series of real numbers.The Golden Ratio is unique because it's an irregular number, which means it doesn't conform to the properties associated with typical numbers, called

**rational numbers**.