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"ultimately converge" is a grammatically correct and usable phrase in written English.
It can be used when describing a process or phenomenon that eventually comes to a common point or conclusion. Example: After years of negotiations and compromises, the two countries ultimately converged on a trade agreement that was beneficial for both parties.
Exact(45)
Public opinion and expert opinion, he argues, ultimately converge on the proper ratings.
All the threads ultimately converge on the "Moral Calculus," which consists of a set of numbered propositions.
In the early 1990s, visionary futurist Terence McKenna hypothesized that two seemingly disparate modalities of consciousness alteration and extension drugs and computers might ultimately converge.
Muscular contraction is the nervous system's only externally directed product, and the signaling routes which pass through the various brain components must ultimately converge on the motor areas.
Inhibition of ERK and FAK blocked mineral deposition on both substrates, suggesting that the observed differences in signaling pathways ultimately converge to the same cell fate.
But an iterative design process requires that there be a number of trial design attempts and divergent changes that will ultimately converge on a design solution.
Similar(15)
"Kafka on the Shore" tells two alternating and ultimately converging stories.
Though radically different in appearance and approach, Mr. Brühl's characters in the two films ultimately converged.
(Also, because the series ultimately converges to the drama of Cooper's return, it leaves its amazingly rich skein of plot lines utterly unresolved).
Although the games suggested that players could influence the unfolding story, like a "Choose Your Own Adventure" book in digital form, the various pathways ultimately converged.
MARY Abel Ferrara's pulp-thin, violence-haunted view of Jesus in media is a clever yet artificial construction that ultimately converges to spiritual banalities.
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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