Status functions

5.2.8 Status functions

bool is_empty() const; 
bool is_whole() const; 
bool is_signed() const; 
bool is_bounded() const; 
bool is_singleton() const; 
bool is_okay() const; 
 
bool has_zero() const;

These member functions inquire the current status of the interval object.

is_empty(): Whether the interval is empty, that is whether $A∈ IR$ is $a= a= ∅$ .
is_whole(): Whether the interval spans the whole $R$ , that is whether for $A ∈ IR$ is $a= -∞ ∧a-=∞$ .
is_signed(): Whether the interval contains a sign, that is for $A ∈IR$ defined as $sgn(a)= sgn(a)$ . It is of note that for this definition it is considered that $-0 ̸= 0$ .
is_singleton(): Whether the interval represents a single value in $R$ , that is for $A∈ IR$ defined as $a= a⇔ a,a∈ R$ .
is_okay(): Determines whether the interval is normalized, if false the interval must be normalized with the respective functions.
has_zero(): Determines whether the interval contains a zero, i.e. whether for a given interval $A ∈ IR$ it is true that $±0 ∈A$ , where this function will return true if either or both of $-0$ and $0$ are in $A$ .

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