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The phrase "are two different approximations" is correct and usable in written English.
You can use it when discussing or comparing two distinct methods or estimates in a mathematical or analytical context.
Example: "The results of the two experiments are two different approximations of the same phenomenon."
Alternatives: "represent two distinct estimates" or "constitute two separate approximations."
Exact(1)
According to their theory, the RSA and quasi-steady state approximation [19], [20] are two different approximations and there are instances where the quasi-steady state approximation can be valid without the RSA.
Similar(59)
Formulas for the amplitude decay are given in two different approximations.
The electron motion is calculated in two different approximations as described in detail below.
Once the features are sorted in a ranking, two different approximations to weight each feature according to its ranking position have been carried out.
In the analytical solution two different approximations are considered.
Two different approximations are proposed that allow the use of MOC as a model reduction technique.
Consequently two different approximations have been proposed.
Then, two different approximations of the optimal solution are carried out to obtain feasible design techniques of the active detector and input signal generator.
Therefore we will give two different approximations in the following.
For further complexity reduction, two different approximation methods are presented.
In the analytical solution three different approximations are used.
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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