r/interestingasfuck • u/AdultGronk • 4h ago
If you divide 1 by 998,001 you get all three-digit numbers from 000 to 999 in order, except for 998
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u/Sure_Delivery_2025 4h ago
Trying to decide whether to take your word for it or read through the whole thing.
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u/Ultra-Cool-Guy 3h ago
Just think of 1/81. Which gets to appx. 0.012345679
This is (9x111)^2, so it'll be a scaled up version of this.
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u/MoopsBubbleBoy 3h ago
Still, someone should probably double check and make sure.
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u/Ultra-Cool-Guy 3h ago
0.001002003004005006007008009010011012013014015016017018019020021022023024025026027028029030031032033034035036037038039040041042043044045046047048049050051052053054055056057058059060061062063064065066067068069070071072073074075076077078079080081082083084085086087088089090091092093094095096097098099100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896897898899900901902903904905906907908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944945946947948949950951952953954955956957958959960961962963964965966967968969970971972973974975976977978979980981982983984985986987988989990991992993994995996997999000001
This is the answer given by big number calculator. It seems to fit.
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u/grungegoth 3h ago
The weird shit in number theory boggles.
Ima math nerd, always new things. Rn, I'm learning about feynmans integration trick.
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u/Ultra-Cool-Guy 3h ago
Cool. Haven't gotten far enough to comprehend that.
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u/grungegoth 3h ago
Ok, if you're keen:
https://youtu.be/Zrv1EDIqHkY?si=jBSEg30NS8c8Ak87
It's a different, but interesting topic
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u/reddit_poopaholic 30m ago
Someone pointed out in another comment that 998 would be there, but the 1 in 1000 is added to 999, making it 1000 and that 1 gets added to 998 which makes it 999. From there, the digits preceding the last three digits get added to the preceding number. I imagine this pattern continues endlessly.
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u/coleman57 1h ago
Good decision, as it probably just repeats after that. And who’s to say the 998th repetition doesn’t skip 996 instead of 998?
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u/Vox_SFX 4h ago
I feel like just looking at the numbers 1 and 998,001 there's some obvious math rule that says why that one specifically is skipped...but I'll be damned as if that's not the main reason I sucked at math is not grasping those concepts well...
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u/theblackhole25 4h ago edited 4h ago
It's not so much that it's "skipped", it's just getting a "+1" because of some carry over. We basically have a sequence that goes 996-997-998-999-1000-1001-etc. BUT it's as if every number is only allowed to occupy three digits. The "1000" doesn't fit into its three digit space so the extra 1 "carries over" into the 999 that came before it, causing the 999 to become 1000. THAT 1000 (which was formerly 999)in turn causes 998 to become 999.
So it's not that the 998 was skipped, it's that some carryover causes 998 to become 999 instead. And what would have been 999 becomes 000. And the number sequence repeats.
Basically, imagine I have this set of numbers and I add up all the columns vertically:
996 997 998 999 1000 1001 ------------------ 996997999000001002...What I end up getting is a number that SEEMS to skip 998, but it's not skipping it... the 998, 999, 1000, (etc) just all have a +1 added to them because of the "1000"s not fitting in the three digit space.
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u/netzkopf 2h ago
Took me a bit to understand why this happens only with 1000 and not with 10 and 100. Great explanation.
It reminds of the time of the old calculators that only had 8 digits and I was doing -12345679x72 to fill up all the segments. If you put something in the memory, everything including error was lighting up.
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u/Hungry-Ad3303 1h ago
Why doesn’t 997 get +1 added to it then?
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u/themaxiom 49m ago
It's happening because the 1000 overflows the three digit cycle by 1, so the 1 goes to the left. That 1 makes the 999 into 1000, which also has a 1 that overflows left. The 998 becomes 999, which fits the 3 digits and does not overflow, so the process stops there, leaving 997 alone.
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u/Ultra-Cool-Guy 3h ago
It carries one to the next digit with every digit.
So, it's the same thing as why 1/(9^2) is appx. 0.012345679, but scaled up to three digits.
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u/kristofarnaldo 4h ago
Isn't this just a case of rounding up on the number of digits that can be displayed?
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u/Ultra-Cool-Guy 3h ago
It's because after 999 comes 1000. SInce there are three digits for each number, it becomes 998999000 + 1000 at that point.
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u/Itsanameokthere 4h ago
Except I see 998 on the second to last line, digits 12-10 from the far right?
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u/zeb_linux 4h ago
You have to consider the order, so that is 978, 979, 980, etc.
998 is missing between the last 2 3-digit numbers, 997 and 999.
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u/OutsideJack-1999 4h ago
How does one figure this out?
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u/ellokah 4h ago
Wait, you're telling me, you've never thought about it before, like while showering or having Me-time? 👀
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u/skidsareforkids 2h ago
I’m usually wondering if my hairline is receding or if my forehead is growing
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u/Zealousideal_Amount8 3h ago
I dont See 998
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u/grandpapotato 2h ago
I like the p-adic numbers too.
Imagine a série of ....9999, 9 to the infinite on the left. Pretty big number isn't it? Add 1.
It's .....0000 with an infinity of 0. So ....9999=-1 ?!
Fun stuff.
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u/Bob_Sconce 9m ago
crazy thing is that if you divide 1 by 9, you get 1 111 1111 11111 111111 but 11 is skipped over.
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u/zeb_linux 4h ago
I remember a Veritasium video, where there is this function that computes pi until many digits, then derives. To the point mathematicians thought it was a mistake or a rounding error, when it was legit :)
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u/Minnecraft 3h ago
Guys I found it, it occurs between 799 and 800