# .999 = 1? **URL:** \ **Category:** Factual Questions\ **Created:** [July 31, 2000, 6:28am UTC](https://boards.straightdope.com/t/999-1/27517 "2000-07-31T06:28:03Z")\ **Posts on this page:** 20\ **Page:** 51
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [October 2, 2012, 5:38pm UTC](https://boards.straightdope.com/t/999-1/27517/1006 "2012-10-02T17:38:54Z")
> [@Leo\_Bloom](#): > > At 1100 AM: Post #1000! Actually, that was post # 999.99999… ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [October 2, 2012, 5:49pm UTC](https://boards.straightdope.com/t/999-1/27517/1007 "2012-10-02T17:49:19Z")
> [@CurtC](#): > > Actually, that was post # 999.99999… True – except that post numbers are ordinal numbers or cardinal numbers, and not real numbers. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 2, 2012, 7:57pm UTC](https://boards.straightdope.com/t/999-1/27517/1008 "2012-10-02T19:57:27Z")
> [@Francis\_Vaughan](#): > > This is just the stuff **Valmont314** wrote, and the subject of the existing conversation. Sadly they don’t add anything new. I agree that **Paradoxical** could be accused of over-zealously flooding the zone. If it’s any consolation–to me it most definitely would be–the number 1001 appears intermittently in Finnegans Wake as the token for infinite number of events, things, people, etc., and their recursions. The most explicit numerological embedding of this is in what have come to be known as the “thunderwords.” Nine are 100 letters long, and the 10th is 101 letters long. (In addition to the many essays on their meaning, a full book is now in [print](http://www.amazon.com/The-Role-Thunder-Finnegans-Wake/dp/0802009239). The comple list of thunderwords is [here](http://www.robotwisdom.com/jaj/fwake/thunder.html). The words can be heard as voiced by a machine [here](http://www.youtube.com/watch?v=QLQsPr-XUng&feature=youtube_gdata_player).) Here is the final, conclusive word (the presence of Norse gods has been noted): FW424: Ullhodturdenweirmudgaardgringnirurdrmolnirfenrirlukkilokkibaugimandodrrerinsurtkrinmgernrackinarockar [/\* \*An artifact of the character display, on my machine at least, incorrectly has the last letter separated by a space from the others. Significant? ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [October 2, 2012, 8:05pm UTC](https://boards.straightdope.com/t/999-1/27517/1009 "2012-10-02T20:05:03Z")
Plus an additional incorrect “[/”. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [October 2, 2012, 8:59pm UTC](https://boards.straightdope.com/t/999-1/27517/1010 "2012-10-02T20:59:49Z")
But guys Here’s an old argument between myself and a friend: Does .9999… (nine repeating forever) really equal 1? I’ve had people swear it does, and try to prove it w/ equations, but the equations just boiled down to saying “.999 =1 is true because 1 = .999”. Can anyone offer any decent proof either way? ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [October 2, 2012, 9:57pm UTC](https://boards.straightdope.com/t/999-1/27517/1011 "2012-10-02T21:57:37Z")
**Moderator Note** As some have suspected, **Paradoxical Paradigm** was a sock of **Valmont314**. I have banned both usernames. He overlooked the fact that 2 + 2 = 4 🙂 Colibri General Questions Moderator ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [October 2, 2012, 10:06pm UTC](https://boards.straightdope.com/t/999-1/27517/1012 "2012-10-02T22:06:43Z")
> [@Jragon](#): > > But guys > > Here’s an old argument between myself and a friend: > > Does .9999… (nine repeating forever) really equal 1? I’ve had people swear it does, and try to prove it w/ equations, but the equations just boiled down to saying “.999 =1 is true because 1 = .999”. Can anyone offer any decent proof either way? You’re kidding, right? Did you read the first 1,000 posts? ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [October 2, 2012, 10:07pm UTC](https://boards.straightdope.com/t/999-1/27517/1013 "2012-10-02T22:07:19Z")
> [@jragon](#): > > can anyone offer any decent proof either way? 10 \* 0.9… = 9.9… 10 \* 0.9… - 0.9… = 9.9… - 0.9… (10-1) \* 0.9… = 9.9… - 0.9… (10-1) \* 0.9… = 9 9 \* 0.9… = 9 0.9… = 1 or 1/3 = 0.3… 3 \* 1/3 = 3\* 0.3… 1 = 0.9… ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [October 2, 2012, 10:14pm UTC](https://boards.straightdope.com/t/999-1/27517/1014 "2012-10-02T22:14:38Z")
> [@CookingWithGas](#): > > You’re kidding, right? Did you read the first 1,000 posts? Read them? He made 38 of them himself. What’s that whooshing sound I hear? ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [October 2, 2012, 11:12pm UTC](https://boards.straightdope.com/t/999-1/27517/1015 "2012-10-02T23:12:11Z")
> [@The\_Hamster\_King](#): > > 1/3 = 0.3… > 3 \* 1/3 = 3\* 0.3… > 1 = 0.9… Too simple, straight forward and easy to understand. Can you tart that up a bit please. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [October 2, 2012, 11:13pm UTC](https://boards.straightdope.com/t/999-1/27517/1016 "2012-10-02T23:13:36Z")
> [@CookingWithGas](#): > > You’re kidding, right? Did you read the first 1,000 posts? Or even just read the [OP again](http://boards.straightdope.com/sdmb/showpost.php?p=618002&postcount=1)! What’s that recursive re-iterative whooshing sound I hear? Why, it’s that very same recursive stuff **V** \*\ ***314** was telling us about! From this point forth, we can simply repeat earlier posts by referring to them by number, or with a link. That will save so much time. Now, GOTO Post #2. Well, maybe GOTO Post #3, where the first (in this thread) meaningful answer may be seen. Proceed from there. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [October 3, 2012, 12:05am UTC](https://boards.straightdope.com/t/999-1/27517/1017 "2012-10-03T00:05:37Z")
> [@Jragon](#): > > But guys > > Here’s an old argument between myself and a friend: > > Does .9999… (nine repeating forever) really equal 1? I’ve had people swear it does, and try to prove it w/ equations, but the equations just boiled down to saying “.999 =1 is true because 1 = .999”. Can anyone offer any decent proof either way? [a](http://boards.straightdope.com/sdmb/showthread.php?t=158752) aaaay! ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [October 3, 2012, 12:42am UTC](https://boards.straightdope.com/t/999-1/27517/1018 "2012-10-03T00:42:10Z")
> [@Jragon](#): > > Can anyone offer any decent proof either way? I can offer an extremely indecent proof, but it violates the two-lick rule. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [October 6, 2012, 12:09am UTC](https://boards.straightdope.com/t/999-1/27517/1019 "2012-10-06T00:09:09Z")
I just thought of something today that might be relevant to this discussion, and in any case I’m curious to know the answer. Suppose you pick a random point on the real number line; what is the chance that the point you picked is a rational number? If there are infinitely more reals than rationals, then apparently the chance would be zero (or “approaches” zero, or some such.) But if the chance were truly zero than it would be impossible to pick a rational, which shouldn’t be the case. If “infinitely unlikely” does not equal zero, then what does it equal? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [October 6, 2012, 12:12am UTC](https://boards.straightdope.com/t/999-1/27517/1020 "2012-10-06T00:12:43Z")
With the uniform distribution on a finite real interval (such as [0, 1]), yes, the probability of picking a rational is conventionally described as 0. On the conventional account of probability, “probability 0” does not mean “impossible”. On the conventional account of probability, simply knowing the probability of an event cannot tell you whether it is impossible or not, any more than it would tell you whether it is desirable or funny or prophesied. This is exactly the same as the fact that, on the conventional account of area, any particular point or line has area 0, even though it has 1 point (in the former case) or even infinitely many points (in the latter case), not 0 points. On the conventional account of area, simply knowing the area of a locus does not tell you whether that locus contains 0 points or not, any more than it tells you whether it is pretty or curvy or in the shape of a letter. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [October 6, 2012, 12:18am UTC](https://boards.straightdope.com/t/999-1/27517/1021 "2012-10-06T00:18:58Z")
Not impossible but it never actually happens? Sounds like getting a carry permit in New York City. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [October 6, 2012, 4:24am UTC](https://boards.straightdope.com/t/999-1/27517/1022 "2012-10-06T04:24:16Z")
It’s like, what is the probability that a randomly-chosen number in [0, 1] would be exactly 0.5637585534264…(i.e., some particular number, rational, irrational, or otherwise). Well, there are infinitely-many equally-probable points, and you are choosing one of them. So the probability is 1/∞ which is generally agreed to be 0. (What else could it be?) And ALL numbers in the interval are equally probable (assuming a uniform distribution, which is just another way of saying that all numbers in the interval are equally probable), that probability being 0. Yet, if you were to choose a number at random, then certainly _some_ particular number will get chosen! This is true even if the distribution is NOT uniform. Even if the distribution were, say, a bell-shaped curve (or any shape), the probability of getting a specific point is 0. Thus, it is fairly meaningless (or roughly so) to speak of this. Rather, we speak of the probability of picking a point within some specific interval like [.4, .6]. This can be calculated, for uniform distributions, or normal (bell-shaped) distributions, or any other shape. Sub-intervals within [0, 1] having a greater probability than other sub-intervals are said to have a higher _probability density_ than surrounding areas. ---
**Author:** ![Bremidon](https://avatars.discourse-cdn.com/v4/letter/b/ac91a4/32.png) [@Bremidon](https://boards.straightdope.com/u/Bremidon)\ **Post date:** [October 6, 2012, 5:53am UTC](https://boards.straightdope.com/t/999-1/27517/1023 "2012-10-06T05:53:51Z")
I rather like the idea that the length of (0,1) = length of [0,1]. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [October 6, 2012, 7:33am UTC](https://boards.straightdope.com/t/999-1/27517/1024 "2012-10-06T07:33:29Z")
> [@Bremidon](#): > > I rather like the idea that the length of (0,1) = length of [0,1]. If I’m not mistaken about this, you could start with the interval [0, 1] and then strike out ALL the rational numbers, leaving only the irrationals – and the remaining length would still be the same. (In other words, the irrationals are so much more numerous than the rationals, that the rationals aren’t even relevant.) ---
**Author:** ![Bremidon](https://avatars.discourse-cdn.com/v4/letter/b/ac91a4/32.png) [@Bremidon](https://boards.straightdope.com/u/Bremidon)\ **Post date:** [October 6, 2012, 4:25pm UTC](https://boards.straightdope.com/t/999-1/27517/1025 "2012-10-06T16:25:00Z")
> [@Senegoid](#): > > If I’m not mistaken about this, you could start with the interval [0, 1] and then strike out ALL the rational numbers, leaving only the irrationals – and the remaining length would still be the same. > > (In other words, the irrationals are so much more numerous than the rationals, that the rationals aren’t even relevant.) Correct. Add the fact that between _any_ two irrationals is at least one rational, and you’ve got the start of a pretty good headache 🙂 [Previous page](https://boards.straightdope.com/t/999-1/27517.md?page=50) [Next page](https://boards.straightdope.com/t/999-1/27517.md?page=52)