The phrase "a number of assertions" is correct and usable in written English.
It can be used when referring to multiple statements or claims that are being made or discussed.
Example: "In her research paper, she presented a number of assertions that challenged the existing theories in the field."
Alternatives: "several claims" or "multiple statements".
"The True and Only Heaven" is marred by a number of assertions that lack firm empirical foundation.
Writer lists a number of assertions made by the Presidents shows how each one of them is false.
His paper contains a number of assertions about what is crucial, without much explanation of why these things are crucial.
The Ergenekon indictment makes a number of assertions that, to put it mildly, don't inspire much confidence in the sophistication of the prosecutors making the case.
"I find a number of assertions, which, at best, demand careful analysis and, at worst, do not deserve any analysis," Mr. Armstrong said.
On Tuesday afternoon lawyers for the NT government put a number of assertions to Carroll that were raised during Voller's testimony – who they were not allowed to cross-examine on Monday.
New Yorkers have read a number of troubling assertions about the charity's finances recently in The Daily News and The New York Times.
The defense secretary listened to the governor's list of complaints and challenged a number of the assertions, in particular on noise pollution, the level of military training conducted here and the Navy's impact on marine wildlife.
At a contentious hearing of the House oversight committee, Mr. Comey acknowledged under questioning that a number of key assertions that Mrs. Clinton made for months in defending her email system were contradicted by the F.B.I.'s investigation.
To the Editor: I object to a number of the assertions in "Leaving the Past Behind" (Feb. 8) about Grenada that suggest that the 1983 United States invasion was justified.
