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?
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