Short answer: the denominator is (10^48 - 10^24 - 1).
Long answer follows.
It's actually easier to understand if you work backwards and arrive at the expression yourself, by asking yourself: "If I wanted the number that starts like
0.0...000 0...001 0...001 0...002 0...003 0...005 0...008 ...
(with each block being 24 digits long), how would I express that number?"
Well, calling the Fibonacci numbers f_n (with f_1=0), that decimal expansion you want is sum (f_n 10^(-24n)) over n≥1. This is sum (f_n x^n) evaluated at x = 10^(-24).
It is easy to work out (especially if you know the trick already) that sum (f_n x^n) = x^2 / (1 - x - x^2), which at x = 10^(-24) gives that the number we want is
1/(10^48 - 10^24 - 1), which is exactly what 1/999999999999999999999998999999999999999999999999 is.
This may be more interesting if you consider more examples:
* if we want the number
0 . 0001 0002 0004 0008 0016 0032 0064 0128...,
then it is sum (2^(n-1) 10000^(-n)). We can calculate that sum(2^(n-1) x^n) is x/(1-2x), which at x = 1/10000 becomes 1/9998. And indeed
1/9998 = 0.0001000200040008001600320064012802560512102420484096...
Similarly,
* if we want the number
0 . 000 001 002 003 004 005 ...,
then it is sum ((n-1) 1000^(-n)). And sum ((n-1) x^n) is x^2/(1-x)^2, and putting x = 1/1000 in it gives 1/999^2 = 1/998001, and indeed
1/998001 = 0.000001002003004005006007008009010011012013014015016...
Basically whenever sum (a_n x^n) has a nice form (aka the generating function of the sequence), you can plug in x = 1/(some power of 10) and get such pretty decimal expansions.
(Edit: Formatting, and the "short answer" at the top.)
If it were Buzzfeed the title would have been something like "You'll never believe what happened when she divided one by 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999!!!!!1"
Yes, and hurray for ad hominems, right? Why discredit the "eli5", just because it's from Reddit? What if it's a useful method to convey what you mean? We just can't use it now, because it's from Reddit?
Also, they didn't say it's bad because it's from reddit, the statement could be interpreted as saying that it's bad, and also that it's from reddit. Imagine http://laurencetennant.com/bonds/adhominem.html applied to the genetic fallacy, and you'll see what I mean.
Some of us here do not use reddit much, so using slang specific to that site can be confusing. In this case, I don't think that saying "eli5" instead "explain" is worth risking this potential for confusion, as only 3 letters are saved.
Yes, except that's not actually what people mean when they type those letters. A five year old has almost zero understanding of math. Where would you even begin?
If you want a simple explanation, just say so. There's really no need to use internet memes for basic communication.
Wow. Based on the responses, you'd think I wrote a style guide that said to use eli5 whenever possible. If you don't like it, don't use it. I don't. I was only pointing out that the abbreviation neither stands for just "explain" nor saves a mere three letters.
I always figured it was supposed to be a single word that started with "eli" followed by 5 letters, in the manner of i18n.
The only English words I could find matching that pattern are elicited, elicitor, elidible, eligible, eligibly, elisions, elitisms and elitists - none of which seem apt, although "elicited" is tantalisingly close. From context I always read it as "elucidate" (elu6?)
"explain like I'm 5" is almost certain to be understood regardless of the reader. "Eli5" is unintelligible unless you are part of a particular, narrow, culture. I had no idea what it meant.
(In truth, the "like I'm 5" part is not obvious so could be misunderstood, but is easier to grasp the meaning.)
Thanks. The ad hominem is a counter-argument; you're discrediting an argument based on a person's character. So "jack is an idiot" is not an ad hominem; "that can't be true, because jack says it, and he's an idiot" is.
I thought the guy meant: "I don't like it because it's from reddit."
But ikeboy has it right: in this case, because reddit is not a person, it's a genetic fallacy, not an ad hominem. Which I didn't even know existed. And, of course, he didn't say that it was because of reddit, so it wasn't even that :)
I'm all for not letting reddit jargon get a foothold here. Reddit culture is downright unlikeable since the entire reason that site seems to exist is to foster echo chambers and cliquish behavior. I'd prefer to keep any vestige of that out of HN. This site is a rare jewel in the sewer of the Internet and it's better that way.
> Why discredit the "eli5", just because it's from Reddit?
Redditit is childish, racist, sexist, ignorant and a hive mind.
eli5 like most things on reddit includes this. There are a lot of under currents in the term.
It shouts it's ok to be 'proud' of being ignorant on a topic.
Rather than the adult, it's ok not to know, just ask someone for a simple explanation. Adults should know you don't need a meme to hide behind to say I'm not good at this.
I'd be very surprised if the majority of people on HN don't also Reddit for our fix of what humans are at their base level but the point is HN is supposed to be better than all that.
>Redditit is childish, racist, sexist, ignorant and a hive mind.
Some people on Reddit may be that way, but that doesn't mean everyone is. Some people everywhere are that way, still doesn't mean everyone is. Try not to be so hateful.
