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The phrase "assuming the same" is correct and usable in written English
It can be used when you want to indicate that you are considering a particular condition or situation to be unchanged or consistent with a previous statement. Example: "The results of the experiment were consistent, assuming the same variables were controlled throughout the process."
Exact(60)
The next evening he returned, assuming the same clerk would not be working.
Assuming the same trend line, it would be a little over $8 billion through December.
He or she will not become a monarch, assuming the same role as Prince Harry.
That would save me $2,602 over two years, assuming the same 1 percent rate.
If you're 35, it would be worth £21,600 by age 65, assuming the same growth rates.
"If you choose to drink and drive or if you choose to text and drive, you're assuming the same risk".
If a levy failed to pass twice, districts would be locked into assuming the same levy as the year before.
RAFfiller and RAFcrystal were disentangled from the total RAF via two assumptions: (a) assuming the same RAFcrystal to CF ratio in the neat matrix and the PNCs, and (b) assuming the same RAFfiller in amorphous and semicrystalline samples.
So to them they have the same income 3 + 1 p. Now, these ps refer to different time periods, but we're assuming the same.
Because it's twice as difficult, it should take twice as long on average to win, assuming the same amount of play is occurring.
Finally, we recorded the number of derived state origins using Fitch parsimony (assuming the same number of steps for gains and reversals).
More suggestions(20)
embracing the same
supposing the same
accepting the same
incorporating the same
assuring the same
assuming the identical
suggesting the same
undertaking the same
asserting the same
understanding the same
realising the same
using the same
resuming the same
demonstrating the same
guaranteeing the same
acknowledging the same
administering the same
arguing the same
believing the same
suppose the same
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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