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The phrase "achieve the same purpose" is correct and usable in written English.
You can use it when discussing different methods or approaches that lead to the same outcome or goal.
Example: "Although the two strategies differ in execution, they ultimately achieve the same purpose of increasing efficiency."
Alternatives: "serve the same function" or "fulfill the same objective."
Exact(12)
In so doing, we achieve the same purpose with a more positive outcome for all.
Nevertheless, other utility functions and metrics might be used to achieve the same purpose.
One could instead formulate and solve a corresponding optimization problem to achieve the same purpose; however, an appropriate model of the communication behavior is required. .
While we find entirely unpersuasive the Government's parade of horribles regarding the judicial interference in executive affairs presented by an injunction directing the President to comply with constitutional restrictions… declaratory relief is likely to achieve the same purpose.
Here, we exploit a memory-efficient recursive temporal filter to achieve the same purpose (temporal median filtering with a window size less than five frames has ever been tested in this study, but is seen to have an inferior performance).
In the last section of the paper, the proposed procedure is compared with another method used by the authors in the past to achieve the same purpose: in situ outdoor measurements attempting to recreate free field conditions.
Similar(47)
Even though protein-folding proteins are expressed at different times and differently between species during the larval stages, they may achieve the same purposes in quality control of nascent protein synthesis and in immune defense.
We find it interesting both from a theoretical as well as practical point of view to develop a similar expansion which can be computed using the classical Fourier coefficients, but achieves the same purpose.
This sweater by Dex Grey at Blonde LA ($110) achieves the same purpose with a bit more of a downtown feel.
Our finding of a more frequent inactivation of MIR34B by hypermethylation in LS-associated than sporadic clear cell carcinomas, together with the absence of abnormal p53 in LS-associated as opposed to sporadic clear cell tumors, supports the idea that MIR34B inactivation and abnormal p53 in part function independently to achieve the same tumorigenic purpose.
Although both examples are research intensive narratives by the applicants to establish their credentials in research skills, they achieve the same communicative purpose through two distinctive persuasive strategies: example 1a focuses on the applicants' education trainings and how these trainings have provided him/her with research skills and inspired further curiosities.
More suggestions(15)
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achieve the same thing
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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