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Let A ( x ) = − 2 x for all x ∈ R and T x = 2 x x + 1 for all x ∈ C. Let f : K × K → R be define by f ( u, v ) = 2 ( u − v ) for all u, v ∈ K. Clearly, A is a bounded linear operator, F ( T ) = { 1 } and A ( 1 ) = − 2 ∈ EP ( f ).
Let X = ℕ ∪ {0} and G X × X × X →→ X be define by G ( x, y, z ) = x + y + z ; if x, y, z are all distinct and different from zero, x + z ; if x = y ≠ z and are all different from zero, y + z + 1 ; if x = 0, y ≠ z and y, z di from zero, y + 2 ; if x = 0, y = z ≠ 0, z + 1 ; if x = y = 0, z ≠ 0, 0 ; if x = y = z.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com