I can't say I've ever given that much thought. I'll just go with whatever you think🙏🏻.
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It's not hard to follow, if you just reason it through. Maybe the tricky part is realizing there are finitely many 60 letter or less combinations of letters, a subset of which are meaningful and define a positive integer (rest are gibberish as far as we're concerned). This can only refer to a finite set of numbers, so there are ones not defined. The least of these satisfies above short sentence. Contradiction.
Its a novel twist on a typical flavor of paradox, to me anyway. Neat
My brain isn't firing on all cylinders today so I'm just defering to your (Almost certainly correct) explanation😎.