[queuebert]

> e is the unique real number satisfying 1 + x <= e^x for all x.

I think if you replace e by 2e, this still holds. Therefore your definition of e is not unique.

[FabHK]

1 + (-0.1) = 0.9

(2e)^(-0.1) = 0.844243...

The former is not <= the latter.