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The phrase "almost infinite number" is correct and usable in written English.
It can be used when describing a quantity that is extremely large but not truly infinite, often in a mathematical or theoretical context.
Example: "The possibilities for creative expression in art are an almost infinite number, limited only by the artist's imagination."
Alternatives: "virtually limitless number" or "nearly infinite quantity".
Exact(52)
London demands that you hold an almost infinite number.
Within this framework, though, there is an almost infinite number of ways of solving the same problem.
Turkey has so many historical sites and an almost infinite number of ancient artifacts, that it has trouble cataloging them, much less protecting, studying and displaying them.
Alejandro Zambra's Multiple Choice (translated from the Spanish by Megan McDowell) goes further: it consists of an almost infinite number of books.
Because the signal itself is digital, you can make an almost infinite number of copies of copies, each as bright and beautiful as the first.
One of the great attractions of Lego is that it can be transformed into an almost infinite number of models with almost infinite shapes and forms.
Similar(8)
Generally speaking, Western writing, or printing, is accomplished by the use of a relatively small number of individual letters capable of being grouped in almost infinite numbers of meaningful permutations.
Additionally the DNA of all participants is stored in a cell line repository, enabling almost infinite numbers of molecular genetic ADHD studies in the future.
Researching other peoples' careers teaches you that there are an almost infinite numbers of ways that you can get into advertising, for example, or become a merchant.
An almost-infinite number of these snow-topped ice floes, a few metres thick above water but many more underneath, surrounded us and dotted the ocean all the way to the horizon.
There are almost an infinite number of combinations of the Rubik's Cube.
More suggestions(16)
virtually infinite number
almost limitless number
almost embarrassing number
almost infinite narrative
almost infinite complexity
almost infinite potential
almost uncountable number
almost infinite direction
almost infinite exploration
almost staggering number
almost arbitrary number
almost infinite channel
almost infinite set
almost infinite combination
almost infinite slack
almost infinite range
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com