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The phrase "both exist" is correct and usable in written English.
You can use it when discussing two entities or concepts that are present or real at the same time.
Example: "In this theory, both exist simultaneously, challenging our understanding of reality."
Alternatives: "both are present" or "both are real".
Exact(60)
Well, in one sense, they do: they both exist so they both have the property of existence.
But they both exist.
Both exist on both sides.
Both exist for the sake of money.
Both exist to serve his interests.
I think both exist in his head.
Not primarily because of racism or Islamophobia, though both exist.
He's both good and evil and I believe they both exist in everyone I've ever met.
Apart from their actual, physical selves, both exist as constructs, expressions of the mind.
Yet Victoria has found its place, and they both exist happily".
Furthermore, libnrnpython3 and libnrnpython2 both exist on my machine, and appear entirely intact.
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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