# Does 0.999... = 1 **URL:** \ **Category:** Factual Questions\ **Created:** [February 14, 2020, 1:26am UTC](https://boards.straightdope.com/t/does-0-999-1/847915 "2020-02-14T01:26:20Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 14, 2020, 1:26am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/1 "2020-02-14T01:26:20Z")
In mathematics, 0.999… = 1 0.999… = (3) x (0.333…) 0.999… (3) x (1/3) 0.999… = 1 In physics, 1 - 1 ≠ 0 because it’s impossible for any two entities to be exactly identical. Let x = 1 - (0.999…) Would it be possible to define x ? ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [February 14, 2020, 1:29am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/2 "2020-02-14T01:29:41Z")
> [@EastUmpqua](#): > > In physics, 1 - 1 ≠ 0 because it’s impossible for any two entities to be exactly identical. Unless physics is now using a very unusual number system, this isn’t true. I think you’re confusing the idea of numerical representation with the idea of significant figures. > [@](#): > > Let x = 1 - (0.999…) > Would it be possible to define x ? You don’t have to define x, you just have to define the rules of your number system and operations in order to calculate x. In the standard everyday real numbers, x would equal zero. ---
**Author:** ![Chingon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chingon/32/17645_2.png) [@Chingon](https://boards.straightdope.com/u/Chingon)\ **Post date:** [February 14, 2020, 1:32am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/3 "2020-02-14T01:32:48Z")
Oh Lord not again… ---
**Author:** ![wolfman](https://avatars.discourse-cdn.com/v4/letter/w/a8b319/32.png) [@wolfman](https://boards.straightdope.com/u/wolfman)\ **Post date:** [February 14, 2020, 1:34am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/4 "2020-02-14T01:34:08Z")
> [@EastUmpqua](#): > > In physics, 1 - 1 ≠ 0 because it’s impossible for any two entities to be exactly identical. Are you using identical in the sense of occupying the same position in time/space? ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [February 14, 2020, 1:39am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/5 "2020-02-14T01:39:24Z")
> [@Chingon](#): > > Oh Lord not again… Yes, seem to recall a very long thread on this subject… ---
**Author:** ![wolfman](https://avatars.discourse-cdn.com/v4/letter/w/a8b319/32.png) [@wolfman](https://boards.straightdope.com/u/wolfman)\ **Post date:** [February 14, 2020, 1:46am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/6 "2020-02-14T01:46:21Z")
> [@Crafter\_Man](#): > > Yes, seem to recall a very long thread on this subject… But was it very long, or infinite? ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 14, 2020, 1:46am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/7 "2020-02-14T01:46:55Z")
> [@Chingon](#): > > Oh Lord not again… I would be very interested in reading the previous thread. How do I find it? ---
**Author:** ![bobot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bobot/32/21622_2.png) [@bobot](https://boards.straightdope.com/u/bobot)\ **Post date:** [February 14, 2020, 1:47am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/8 "2020-02-14T01:47:53Z")
🙂 I say… (won’t. no I won’t.) ---
**Author:** ![moes\_lotion](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@moes\_lotion](https://boards.straightdope.com/u/moes_lotion)\ **Post date:** [February 14, 2020, 1:50am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/9 "2020-02-14T01:50:32Z")
> [@EastUmpqua](#): > > In mathematics, 0.999… = 1 > 0.999… = (3) x (0.333…) > 0.999… (3) x (1/3) > 0.999… = 1 > In physics, 1 - 1 ≠ 0 because it’s impossible for any two entities to be exactly identical. > Let x = 1 - (0.999…) > Would it be possible to define x ? In a fairly recent thread on this, we could have said that your x equaled the probability that the OP (in the other thread) would ever admit that their line of reasoning was invalid ---
**Author:** ![EastUmpqua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eastumpqua/32/6025_2.png) [@EastUmpqua](https://boards.straightdope.com/u/EastUmpqua)\ **Post date:** [February 14, 2020, 2:06am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/10 "2020-02-14T02:06:43Z")
There seem to be problems describing GR and QM using current mathematics because 1/0 and 1/infinity are undefined. Zero defined as a unit-less constant based on the Planck constant could maybe help define 1/0 and 1/infinity. ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [February 14, 2020, 2:11am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/11 "2020-02-14T02:11:36Z")
> [@EastUmpqua](#): > > I would be very interested in reading the previous thread. How do I find it? [https://www.google.com/search?hl=en&as\_q=0.999&as\_epq=&as\_oq=&as\_eq=&as\_nlo=&as\_nhi=&lr=&cr=&as\_qdr=all&as\_sitesearch=https%3A%2F%2Fboards.straightdope.com%2F&as\_occt=any&safe=images&as\_filetype=&as\_rights=](https://www.google.com/search?hl=en&as_q=0.999&as_epq=&as_oq=&as_eq=&as_nlo=&as_nhi=&lr=&cr=&as_qdr=all&as_sitesearch=https%3A%2F%2Fboards.straightdope.com%2F&as_occt=any&safe=images&as_filetype=&as_rights=) ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [February 14, 2020, 2:29am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/12 "2020-02-14T02:29:25Z")
> [@EastUmpqua](#): > > There seem to be problems describing GR and QM using current mathematics because 1/0 and 1/infinity are undefined. Zero defined as a unit-less constant based on the Planck constant could maybe help define 1/0 and 1/infinity. The title question is answered comprehensively in the previous thread. As for the additional questions, Planck’s constant is in fact non-zero (that is kind of the point!). You can even work in a system of units where it equals 1 or 2π or something. And if there is a question concerning renormalization, which is an interesting topic, I will leave it to you to ask. ---
**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:** [February 14, 2020, 3:09am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/13 "2020-02-14T03:09:50Z")
Physics uses math as a language. Math is more fundamental. More importantly, math is defined and subject to proofs. The role of zero in mathematics has been investigated and rigidly defined in many ways. Math has a huge number of internally consistent forms that are not what are taught in high school, and some of them have been shown to be extremely useful in solving some physical problems. I don’t know of any that redefine zero that are of use in GR and QM, though. Nevertheless, I doubt finding one would solve your issue. > [@](#): > > In physics, 1 - 1 ≠ 0 because it’s impossible for any two entities to be exactly identical. This is absolutely wrong. AFAIK, all individual subatomic particles are identical to one another of the same type. You’re probably thinking of the Pauli exclusion principle, which forbids two particles from occupying the same quantum state. But that’s applicable only to fermions. Multiple bosons can have one quantum state. And even so, that 1-1 = 0 has nothing to do with that, either. All physics obeys basic arithmetic. ---
**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:** [February 14, 2020, 4:11am UTC](https://boards.straightdope.com/t/does-0-999-1/847915/14 "2020-02-14T04:11:27Z")
> [@EastUmpqua](#): > > I would be very interested in reading the previous thread. How do I find it? [Moderating] Please read the linked threads. Since we have discussed this many times before, I’m going to close this for now. If you have additional questions after reading the threads, PM me and I will consider reopening this. Colibri General Questions Moderator