Pensieve header: Computing an approximation to the set of fusible numbers.

FN={0};
Fuse[a_,b_]:=If[Abs[a-b]≤1,(a+b+1)/2, 0];
Do[
FN=FN⋃(Fuse@@@Tuples[FN,2]),
{10}
];
FN

?Tuples

f@@@Tuples[Range[5],2]

? /@

?@@@

?ListPlot

ListPlot[FN]

NumberLinePlot[FN]