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If (rpreccurlyeq f(r)) for some (rin X), then f has a unique fixed point in X. (The space X in this statement is not obligatory complete).
If (f(r preccurlyeq r) for some (rin X), then f has a unique fixed point in X. (The space X in this statement is not obligatory complete).
If (f(r preccurlyeq r) for some (rin X), then f has at least countable or finite fixed points in X. (The space X in this statement is not obligatory complete).
If (rpreccurlyeq f(r)) for some (rin X), then f has at least countable or finite fixed points in X. (The space X in this statement is not obligatory complete).
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This statement is not clear.
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This statement is not correct, however.
But this statement is not correct.
This statement is not arguable.
" This statement is not always correct.
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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