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The phrase "approach the ultimate" is correct and usable in written English.
It can be used in contexts where one is discussing striving towards a final goal or peak achievement.
Example: "In our quest for innovation, we must always strive to approach the ultimate in technology and design."
Alternatives: "reach the pinnacle" or "attain the highest point".
Exact(13)
Our objective is to devise the new quantum algorithms and protocols needed to approach the ultimate performance bounds of quantum information systems.
Here, amplitude-squeezed light can in principle mitigate the effects of a finite detection efficiency26 and allow the measurement to more closely approach the ultimate quantum limit where nadd = 1/2.
"It's an effort on the part of the U.S. to convey a willingness to re-energize the dialogue about beef, to convey a sense of flexibility in how we approach the ultimate reopening of this market," Mr. Vilsack said Wednesday in an interview.
For the capability approach, the ultimate ends of interpersonal comparisons are people's capabilities.
This result now allows me to continue moving further into the project and approach the ultimate goal of solving a structure.
Rather, they approach the ultimate purchase through a process or series of steps in which the actual purchase is but the final threshold.
Similar(47)
In sum, the three mini-players mentioned here are very good, though none approaches the ultimate limits of performance.
The measurement precision approaches the ultimate Heisenberg limit as attains the minimum in an ideal Dicke state.
And they fairly gape at how close the polls show Mr. Bush to be approaching the ultimate level, the presidency, with his same soft-edged wares.
While test specimens without constrained plates showed the minimum ultimate shear strain, test specimens with 25 mm-thick wooden constrained plates showed the maximum, approaching the ultimate shear strain of the web's steel in material property test.
The calculation method clearly quantifies the differences in shear behaviour of the investigated beam cross-sections and approaches the ultimate shear capacity of all beam types relatively well, which proves this a valuable approach also for other hybrid beam types.
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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