According to the definition of rational numbers, we can represent any rational number \(x\) by two integers \(a,b\), with \(b\neq 0\), formally \(x=\frac ab\).
Based on the order relation for integers, we have three cases of representing a rational number, called:
Based on the definition of subtraction of rational numbers, we can define the order relation for rational numbers as follows:
Corollaries: 1
Definitions: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Proofs: 17 18 19
Propositions: 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
The first $0$ in all three cases means the rational zero, the second $0$ means the integer zero. ↩