I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
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Also you never said why you'd pick the 100s.
I see I made a mistake by acknowledging your argument, and trying to indicate my understanding there of, before trying to get back to the point at hand that an infinite number of $1 bills is worth the same amount as an infinite number of $100 bills.
I won't make the same mistake again.