A long, long time ago (like a hundred or so) mathematicians were having fun and creating set theory, and then some smartass like Mr Russel and his friends came along and started saying things like "what happens if I take the set of alllllll sets ever?" and "what happens if I take the set of all sets that don't belong to themselves?" and "lol paradoxes" AND THEY BROKE THE MATHEMATICS. People were very sad and they had to build up the mathematics again, only this time they made it better so it wouldn't be broken any more.
So in this course I am studying how to build stuff like natural numbers (which are 1, 2, 3, etc...) and then addition and then multiplication and so on and so on. EXCEPT THAT I AM BUILDING THE ADDITION WITHOUT THE ZERO BECAUSE OOOPS I'M NOT CONSIDERING ZERO AS A NATURAL NUMBER. It makes no sense to leave the zero out because all of the beautiful properties of the zero? Out of the window. My prof said we could include the zero, or start from one, and it was a matter of preference, but I think I'd very much prefer to keep the zero tysm. Suddenly I remember why I stopped going to her lessons.
Among my (few) pages of notes there's scribbles in the margins that look suspiciously like "PROVE THIS THEOREM BECAUSE YOU WERE SLEEPING WHILE SHE TALKED" and "NOT ENOUGH COFFEE TODAY".
So I figured I'd use the provided material instead of relying only on my awesome notes. Except the materials are a dozen or so handwritten and scanned pdfs that the prof put online, which are also not in order, unless you count "ZF, 1, 3, 4', 4, 5, 6a, 6b, 7, 10a, 10b, reals, math system" to be an order. (It's not, math system comes before chapter 1 from what gathered.) In a course about numeration systems. The irony is killing me.
This is a fucking puzzle worth 1000 picarats.
Except, wait, it's one of my exercises taken from the awesome pdfs of not awesome. I'd give cookies to anyone who can solve it, except I'm fairly sure it's impossible because each letter is a different digit (from 0 to 9) and the letters are A, B, C, D. WHY IS THERE AN E. THERE CANNOT BE AN E. WHAT DOES THIS EVEN MEAN.