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The phrase "number of ideas" is correct and usable in written English.
You can use this phrase when you want to refer to a specific quantity of ideas. For example, "We discussed a number of ideas in the meeting."
Exact(60)
There are a number of ideas.
I have a number of ideas.
In my opinion the answer is quite simple: It's the number of ideas you develop, the number of ideas you try out, the number of ideas you commission.
Laguerre had a number of ideas to ramp up sales.
We received large number of ideas for an alternative anthem.
Michalevsky and co have considered a number of ideas.
"What I did was package in a useful way a number of ideas.
Or does Frank Miller just have a very limited number of ideas that turn him on?
"There will be any number of ideas on how to spend that money," Mr. Palmer said.
I had a number of ideas kicking around for The Wrong Trousers, which followed in 1993.
"I get hopelessly involved in words to contain the increasing number of ideas….
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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