-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

-1//3 julia> -4//-12 1//3CHAPTER 7. COMPLEX AND RATIONAL NUMBERS 46 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

2//3 julia> -4//8 -1//2 julia> 5//-15 -1//3 julia> -4//-12 1//3 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real

2//3 julia> -4//8 -1//2 julia> 5//-15 -1//3 julia> -4//-12 1//3 This normalized form for a ratio of integers is unique, so equality of rational values can be tested by checking for equality of the immutable type (except that we omit the constructor here for simplicity), representing an exact ratio of integers: struct Rational{T<:Integer} <: Real num::T den::T end It only makes sense to take ratios of integer values, so the parameter type T is restricted to being a subtype of Integer, and a ratio of integers represents a value on the real number line, so any Rational is an instance of the Real