abs(e^iπ^) + abs(i^2^)
this post was submitted on 28 Sep 2023
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\tan(\pi/4) + 1/42 \int_{-7\ln 6}^\infty \exp(-x/7) \dd{x}
The standard way when using ordinal arithmetic is: Take the ordinal 1, which is {{}}. Replace each element with a ordered pair of the form {{a},{a,b}} with second element being 0 (that is {}). Repeat with second element 1. Take a union. Take find the ordinal with this order. Overall: otp({ {{{}},{{},{}}}, {{{}},{{},{{}}}} }) Or simplified
otp({ {{{}}}, {{{}},{{},{{}}}} })
Most of them.
I saw somewhere that someone had decoded how an AI had learnt to do basic arithmetic. And it appeared to be using a massive expression containing lots of sin & cosines to do basic addition
(10^googol^)^0^ + (TREE(3))^0^
Although that's fairly easy to write. It's hard to calculate, if you calculate the brackets first.
Perhaps: (lim_{n->\infty} \sum_{m=1}^n 1/2^m ) + dim(Im(matrix([1,3,4],[2,6,8],[3,9,12])))
(fix add a b := match a with O => b | S x => add x (S b) end) (S O) (S O)
Pi/pi + pi/pi