Status functions

bool is_empty() const; 
bool is_whole() const; 
bool is_singleton() const; 
bool is_okay() const;

These functions return the status of the current interval $k$ , is properly $k ∈RC$ .

is_empty(): Whether the interval is empty i.e. $ℜi,ℑi̸= ∅$ .
is_whole(): Whether the interval spans the whole complex space $(ℜi,ℑi̸= ∅)∧(|ℜi,ℜi,ℑi,ℑi| = ∞) --- --$ .
is_singleton(): Whether the interval refers to a single complex number. $(ℜi,ℑi̸=∅) ∧(ℜi= ℜi)∧(ℑi=ℑi) --- --$ .
is_okay(): Whether the interval is properly defined.