Non-transparent, anonymous currency with no set amount of units that you can’t verify.

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Oh, it's really cool to hear that you've actually went through and verified every transaction that's ever occurred on the Bitcoin blockchain to make sure they balance. cudos to you... Actually, I'm assuming that you trusted the Bitcoin software to make sure that the supply is correct. In which case, your argument is moot because Monero's software can do the same thing.

How many units are currently in circulation?

18,445,342

Less than Bitcoin

I’ll rephrase. It’s a private digital currency.

Indeed