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The phrase "always exists for" is correct and usable in written English.
It can be used to indicate that something is perpetually available or applicable in a certain context or situation.
Example: "In the realm of science, curiosity always exists for those who seek knowledge."
Alternatives: "is always present for" or "always applies to".
Exact(22)
It's pretty straightforward stuff, proving that a new generation always exists for the musical outpourings of tongue-tied boys with ringing guitars.
Such a pair always exists for any.
The radial solution always exists for any (p>1), it is unique and radially non-degenerate.
The solution of the corresponding matrix-valued IVP, always exists for, even is not regressive.
It is well known that (A^{dagger}) always exists for any A and is unique; see, e.g., [3 5].
Nevertheless, the potential always exists for unknown variations in the character of sub-pixel topography (among other uncertainties such as albedo variations) to introduce errors.
Similar(38)
Surname recognition methods rely on low levels of interethnic marriages and the existence of distinctive surname nomenclatures (which do not always exist for some ethnic groups, eg, Black populations in the USA).
"Those opportunities don't always exist for our children".
Among other things, the report acknowledges that dangers have always existed for illegal migrants.
The reality is that choice has always existed for the rich few and is something to which everyone aspired.
"There is power for a woman involved with a younger, less-educated, open man," she asserted, "power the way it has always existed for men in similar circumstances".
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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