#lean #math #code4math

Can one then show that 1 = 2, say by manipulating a - (a + 1) = 0 into a = a + 1, adding 1 to both sides, and subtracting a? No! The reason why is that LEAN knows that subtraction in the naturals isn't subtractive. (Or rather it doesn't think that it is subtractive).

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The proof in LEAN is very simple: tell it to use 0. What happens behind the scenes is that, in LEAN, 0 - 1 = 0 (when considered in natural numbers). I think this is because it's convenient to have naturals closed under basic operations.

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+1 for Secret Mall Apartment

It definitely contributes to math-as-mysticism, incantations done by all-knowing mages that is intractable to mere mortals. But this is far from the truth! And we want more people to recognize that mathematical thinking is useful and approachable and worthwhile!

And also this was the source of bsky.app/profile/davi...

I wrote about this some here.

davidlowryduda.com/paper-fibona...

Thanks. I've never heard of Ologs before.

I appreciate the tip, thanks!