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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

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

)

@QiaochuYuan

Aug 12, 2020

2. the sum of zero terms (the empty sum) is 0; the product of zero terms (the empty product) is 1

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

)

@QiaochuYuan

Aug 12, 2020

3. the degree of the zero polynomial is -∞

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

)

@QiaochuYuan

Aug 12, 2020

4. the maximum of zero numbers is -∞; the minimum of zero numbers is +∞

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Tweets Space Rat

@TetraspaceWest

Aug 12, 2020

if you combine two sets of numbers, the minimum of the combined set is the lesser of the minimums of the two sets. any set combined with 0 objects is itself.

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

)

@QiaochuYuan

Aug 12, 2020

yep. "max" and "min" are operations defined for sets of numbers, not just pairs of numbers, and they should have the "clumping" property that you can replace any subset of such a set with its max or min without affecting the final result, including the empty subset

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

Replying to

and

you can use this same logic to justify both the determinant example and the empty sum and empty product examples, it's a very common meta-pattern

10:18 PM · Aug 12, 2020Twitter Web App

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