The key to remember is that you can’t check a claim about an infinite set by checking a finite set of its elements, no matter how large the finite set.
Should the last sentence be no matter how large the finite set is? Or both forms are correct?
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Answered in the comments:
"Both versions are fine. It's just the standard "linguistic device" called deletion [of predictable / repeated elements]. In your context, the relevant noun is just as predictable as the verb, so that final clause could quite naturally have been reduced to just ...no matter how large." – FumbleFingers