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The phrase "escalating number" is correct and usable in written English.
It is used to describe a situation in which the number of something is steadily increasing. For example, "There has been an escalating number of climate change-related disasters in recent years."
Exact(44)
It is now almost certain that there will be an escalating number of attacks, Mr. Woodcock said.
There is an escalating number of attacks by Taliban remnants who are crossing the border into Afghanistan and attacking U.S. troops stationed there.
The UN protested at a "complete absence of accountability" for the escalating number of civilian deaths in Gaza, saying "the rule of the gun" had taken over.
But the U.N. has been documenting an escalating number of attacks against U.S. and humanitarian aide workers, and also a huge resurgence in the opium trade.
In a country where family bonds mean everything, where second cousins are like siblings and great uncles can be treated like patriarchs, the escalating number of abductions has shaken Colombia to its very core.
In extreme cases, the lure of the luxury journal can encourage the cutting of corners, and contribute to the escalating number of papers that are retracted as flawed or fraudulent.
Similar(14)
"SPF 100 is not just an escalating numbers game," she said.
Kill 850 people and save 5,692 others, still another says in a simultaneously funny and chilling litany of escalating numbers.
The atmosphere has been rarified further by escalating numbers of terrorist bombings — a la Iraq, a la Afghanistan.
The escalating numbers on the dazzling surface of the light board could be counting them, a tally of Mr. McGregor's endless supply of ideas.
And yet nobody here can forget or ignore the escalating numbers of Ebola cases in Sierra Leone, where the epidemic, apparently in check in Liberia and Guinea, is out of control in Freetown's western areas and Port Loko to the north.
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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