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Sep 25, 2020

if you repeatedly square the number 5 the last n digits eventually stabilize for every n and you get a number with infinitely many digits going to the left that squares to itself. it ends ...890625

{soubriquet}

@altachron

Sep 25, 2020

? how would you get a number with infinite length? I would have said it was unbounded but finite? plus like n>1 => n^2>n, so how could you have a (large) integer that squares to itself?

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

Replying to

and

well it's not an integer! it's something wackier called a 10-adic number

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

)

@QiaochuYuan

· Sep 25, 2020

Replying to @QiaochuYuan and @default_friend

these numbers are called 10-adic numbers and they are weird and good. mathematicians work almost exclusively with versions of this construction involving a prime base though google.com/search?q=10-ad

7:10 PM · Sep 25, 2020Twitter Web App

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and

hm, interesting that changing the metric on the set of integers (which seems to be basically what this is doing? could be off base here) actually changes what notations you can use for individual elements