I think it’s more because the float curve was just linear and so the factor makes no difference… because “the mapping” is already linear… (like the shown “curve”)
So now i see why is i shouldn’t have participated in this when in fact doing something totally different and just making break and try to “relax” on BA … because (now) it all makes sense and in fact i should/do know this:
The Float Curve node does make a mapping like in In mathematical notation with real numbers from ℝ: [0,1] -> [0,1] according to “the curve”.
And there is also a (only) linear mapping between the original input and this mapped result determined byt he Factor within [0…1] so that 0.0 → original / 0.5 → “half-mix” between original and mapping / 1.0 → mapping
…and because we are using a computer this is of course a float value… and not a real number
There is a difference between the “real” (and in fact rational) number 1/3 and some represention like 0.33333… because when you multiply both by 3 then you got:
1/3 * 3 = 3/3 = 1
0.3333 * 3 = 0.99999
and the float type standing for a specific floating point represention also uses some base and exponent and so you can not re-present some values correctly ( i have to look up which exactly…)
So in mathematics everything is fine an “rounds up” ( ← pun ) but in the floating representation you got sometimes some not exact values.
( if i remember correctly in some earlier versions of blender you can even see this with the default cube when selecting some vertices/sides… the were not at position ±1 but something like ±0.999999999 )
…also pi or e are real even if infinitly… but i or sometimes j is imaginary…
… because (now) it all makes sense and in fact i should/do know this:
