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   mark (atleagle@mastodon.online)'s status on Friday, 31-May-2024 21:37:16 JST mark

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   • Nick
   • Ben again!
   • Paul Martin
   • Marten
   • Arthur Detoo

   @marten @TheBreadmonkey @nowster @tedric @Nickiquote yep. Hotel infinity works for fractions, but not decimals

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     Marten (marten@mstdn.social)'s status on Friday, 31-May-2024 21:37:24 JST Marten

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     • Nick
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     @TheBreadmonkey @nowster @tedric @Nickiquote my puny brain thinks of it like you could sit there and keep counting 1, 2, 3... it'd take infinitely long but you could.

     You can't sit there and count all real numbers like 0.0000001, 0.0000002. Because between any two of those you could think of, there's always more numbers. Infinitly more numbers in fact. There's simply not a "the next number" after 0.

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     Ben again! (thebreadmonkey@beige.party)'s status on Friday, 31-May-2024 21:37:25 JST Ben again!

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     • Nick
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     @nowster @tedric @Nickiquote

     I'm sorry. At this stage my brain has shut down and I just read that as pie squirt and did a little chuckle. I will attempt to re-read. OK. Different classes of infinites. How?

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     Paul Martin (nowster@fosstodon.org)'s status on Friday, 31-May-2024 21:37:26 JST Paul Martin

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     • Nick
     • Ben again!
     • Arthur Detoo

     @TheBreadmonkey @tedric @Nickiquote Nobody can properly get their heads round infinities. Those things are just weird.

     Rational numbers (fractions) are "countable" but irrational numbers (eg. e, pi, sqrt(2), etc.) are part of a larger class of infinities.

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     Paul Martin (nowster@fosstodon.org)'s status on Friday, 31-May-2024 21:37:27 JST Paul Martin

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     • Nick
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     • Arthur Detoo

     @tedric @TheBreadmonkey @Nickiquote Even more mind blowing is that both "all integers" and "all even integers" are infinities of the same size (countable numbers: aleph null). There's always a mapping from x to 2x.

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     Ben again! (thebreadmonkey@beige.party)'s status on Friday, 31-May-2024 21:37:27 JST Ben again!

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     • Nick
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     @nowster @tedric @Nickiquote

     OK this I did not understand

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     Arthur Detoo (tedric@dads.cool)'s status on Friday, 31-May-2024 21:37:35 JST Arthur Detoo

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     • Nick
     • Ben again!

     @TheBreadmonkey @Nickiquote apologies if this further hurts your brain, but one of the coolest math facts IMO is that you can have bigger and smaller infinities. Like "all integers" is twice as big as "all even integers" even though both sets are infinite

     or "the set of all infinite sets" which sounds by definition like the biggest infinity of all, but then again -- isn't the concept that there's always a way to pack at least *a little* more in? -- "the set of all infinite sets + 1", etc.

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     Ben again! (thebreadmonkey@beige.party)'s status on Friday, 31-May-2024 21:37:36 JST Ben again!

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     • Nick

     @Nickiquote

     Lol. I'd guess someone cleverer than me could tell us, but yes I imagine that almost infinite would have to be the same as infinite. In fact - any measurement in relation to infinite would have to be by definition also infinite, even if it was 1% of infinite. Owwwww my brain hurts.

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     Nick (nickiquote@mstdn.social)'s status on Friday, 31-May-2024 21:37:38 JST Nick

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     • Ben again!

     @TheBreadmonkey I’m wondering whether it’s possible to be almost infinite without being infinite, because like infinity you can’t fix a number as almost infinite.

     Anyway, David Beckham’s 18 goal Premiership record from direct free kicks is less impressive if it turns out the goalmouth is larger than the universe itself. I always knew he was overrated.

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     Ben again! (thebreadmonkey@beige.party)'s status on Friday, 31-May-2024 21:37:39 JST Ben again!

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     I realise I've mixed my metaphors here and that footballers are not scoring goals to win votes. But wouldn't that be a fun idea! Teddy Sheringham for PM! (I don't watch a lot of football)

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     Ben again! (thebreadmonkey@beige.party)'s status on Friday, 31-May-2024 21:37:40 JST Ben again!

     If I were a Labour Party facing an almost infinite open goal, I would simply not choose to make terrible unforced mistakes that alienate huge swathes of my voting base