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Aug 12, 2020

thread: fun facts about zero / the empty set. i will die on all of these hills 1. 0^0 = 0! = {0 choose 0} = 1, these are all variations of the same fact which is that there's a unique function from the empty set to itself, which does nothing. this function is not constant

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Eliezer Yudkowsky

@ESYudkowsky

· Aug 12, 2020

How many different ways are there to choose 0 items from an empty set?

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166

James Propp

@JimPropp

Aug 12, 2020

If you want {n choose k} to equal {n choose n-k} for all k (because choosing which ones to select is equivalent to choosing which ones not to select) you’ll want {n choose 0} to equal 1, unless you want {n choose n} to equal 0 because “choosing all options is refusing to choose”.

QC (in Berlin 7/29-??? w/ COVID

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and

you also want the binomial theorem to be true for exponent zero! many such consistency checks

10:52 PM · Aug 12, 2020Twitter Web App

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