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The phrase "for both exists" is not correct in standard written English.
It may be intended to convey that two entities or concepts are present or valid, but the phrasing is awkward and unclear.
Example: "In this context, we must acknowledge that for both exists a common ground."
Alternatives: "for both are present" or "for both are valid".
Exact(1)
The resemblances between above described Tyrol chronology and Schwarzensee manifest among other things in the strong connection that for both exists between latewood maximum density measurements and August–September mean temperature values (Esper et al., 2007).
Similar(59)
Evidence for both mechanisms exists; for example, in a previous study (Sun et al., 2013), neither p300 nor HDACs could be purified together with the RUNX1/ETO complex from t(8 21) cells using high stringency conditions.
For both predictions exists considerable evidence (e.g., Braitenberg and Schüz 1991; Friede 1954; Rockel et al. 1980; Tower and Young 1973).
Either way, the love for both still exists and is nothing you should be stressed over, as long as the boundaries of the relationships are clearly defined.
Both exist for the sake of money.
They both existed for roughly 18 months before being closed in April 2011 and October 2010 respectively.
The results show that the frozen limit and equilibrium limit both exist for all the mixture compositions.
They both exist for a purpose and that purpose is to create.
Let, be real valued functions defined on an interval such that, both exist for all.
That is to say, its expectation and variance both exist for any bounded stochastic variable.
A (positive) solution to (1.1) and (1.2) is called a smooth (positive) solution if and both exist ( for ).
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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