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The phrase "a number of sets" is correct and usable in written English.
It can be used when referring to multiple sets of items or groups in various contexts, such as mathematics, collections, or categories.
Example: "In the experiment, we analyzed a number of sets of data to draw our conclusions."
Alternatives: "several sets" or "multiple sets".
Exact(19)
We also distribute a number of sets of pre-trained word vectors.
The hope is that they will take a number of sets to have for informal reading in class.
First we cluster the speakers in a number of sets and estimate the transformations on each cluster.
Empirical friction factor correlations obtained from a number of sets of crushed rock are presented for two different packing directions.
"LCD viewing angles have gone from poor to good, but there are still a number of sets that are only fair," said Mr. Willcox.
A number of sets of 2 incomplete SOLS (2 ISOLS) (and hence also 4 incomplete mutually orthogonal Latin squares, briefly 4 IMOLS) are also given.
Similar(41)
A number of set piece advertising events (ie writing about film trailers for our ad network) had brought in a couple of lump sum payments.
The few spoken words that the masque had demanded in Elizabethan days expanded into a "text" of a few hundred lines and a number of set songs.
Painters worked within a number of set genres – there are flower painters, landscape painters, still-life artists, portraitists, painters of farmyard animals and sea battles.
If it is one of a number of set rhyme patterns, it may be identified by the name of the poet with whom the set rhyme is generally associated (for example, the Spenserian stanza is named for Edmund Spenser).
It's already on a number of set top boxes that reside in your living room.
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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