What are some complicated ways to write 1+1?
What are some complicated ways to write 1+1?
Kinda like (2/2)+(3/3) but way more complicated
11 comments
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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({ {{{}}}, {{{}},{{},{{}}}} })
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abs(eiπ) + abs(i2)
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Thanks
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How complex you looking? https://en.m.wikipedia.org/wiki/Principia_Mathematica
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Most of them.
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(10googol)0 + (TREE(3))0
Although that's fairly easy to write. It's hard to calculate, if you calculate the brackets first.
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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
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Pi/pi + pi/pi
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Perhaps: (lim_{n->\infty} \sum_{m=1}n 1/2m ) + dim(Im(matrix([1,3,4],[2,6,8],[3,9,12])))
11 comments
\tan(\pi/4) + 1/42 \int_{-7\ln 6}^\infty \exp(-x/7) \dd{x}