I made the cardinal sin of reversing polarity on my jumper cables the other day - that made me feel like a real idiot

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I swapped out the battery and the car now starts fine (it was acting funny on the old battery which was old anyway).
The "charging" light on the dash is not lit up, and the car runs fine. How do I know the car is not just running off the battery? How do I check the
I got a new voltage regulator to begin with, hoping that my alternator was spared from my stupid mistake.