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"a first set of" is a grammatically correct phrase and can be used in written English.
It is typically used to indicate that there are multiple sets of something, and this is the initial or introductory set. Here is an example: "After completing a first set of experiments, the researchers moved on to a more complex set of tests."
Exact(60)
CBAT at the time of publication of a first set of orbital elements.
A first set of simulations compared current clinical implementation of VADs in single ventricle patients.
A first set of experiments is used to determine the dynamic soil and track characteristics.
A first set of spatial criteria was used to design a number of potential sites.
From these findings, we formulated a first set of general qualitative guidelines for planning practices.
A first set of experiments was carried out with the beam passing through the tank.
This paper explores these mechanisms and suggests a first set of propagation mechanisms.
In a first set of experiments animals were monitored to record perinatal outcomes.
A first set of changes that Google announced on Thursday failed to quell the uproar.
A first set of courses is scheduled to be announced in early summer and to start in the fall.
A first set of experiment was performed at low temperature (T = 2 °C) in order to have only geochemical effects.
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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