# Math question: is there a middle number? **URL:** \ **Category:** Factual Questions\ **Created:** [January 11, 2013, 3:06am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818 "2013-01-11T03:06:57Z")\ **Posts on this page:** 20\ **Page:** 2
**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:** [January 12, 2013, 2:55am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/21 "2013-01-12T02:55:32Z")
I’m thinking the middle point should be the mean average of +∞ and -∞ (that is, ((+∞) + (-∞)) / 2). That should work nicely. Working out the actual arithmetic will be left as an exercise for the reader. ---
**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:** [January 12, 2013, 3:14am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/22 "2013-01-12T03:14:24Z")
Somewheres between 0.999… and 1. I read that here in GQ. It was a simple thread. ---
**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:** [January 12, 2013, 3:15am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/23 "2013-01-12T03:15:35Z")
1 is a middling number, often. Oh. Never mind. ---
**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:** [January 12, 2013, 3:28am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/24 "2013-01-12T03:28:00Z")
No, 1 is the loneliest number. If it were in the middle it wouldn’t be lonely. ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [January 12, 2013, 4:05am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/25 "2013-01-12T04:05:56Z")
> [@Exapno\_Mapcase](#): > > No, 1 is the loneliest number. If it were in the middle it wouldn’t be lonely. It’s weird that two can be as bad as one, even though they’re right next to each other. ---
**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:** [January 12, 2013, 4:08am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/26 "2013-01-12T04:08:31Z")
Are you talking about my nephews? ---
**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:** [January 12, 2013, 2:37pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/27 "2013-01-12T14:37:25Z")
> [@Maserschmidt](#): > > It’s weird that two can be as bad as one, even though they’re right next to each other. Actually there are an infinite number of numbers between 1 and 2. ---
**Author:** ![Jake](https://avatars.discourse-cdn.com/v4/letter/j/f475e1/32.png) [@Jake](https://boards.straightdope.com/u/Jake)\ **Post date:** [January 12, 2013, 2:48pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/28 "2013-01-12T14:48:10Z")
> [@Nars\_Glinley](#): > > 42 Well, I guess _Somebody_ had to say it! 🙂 ---
**Author:** ![chowching](https://avatars.discourse-cdn.com/v4/letter/c/f14d63/32.png) [@chowching](https://boards.straightdope.com/u/chowching)\ **Post date:** [January 12, 2013, 2:53pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/29 "2013-01-12T14:53:23Z")
All numbers are middle numbers. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 12, 2013, 3:19pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/30 "2013-01-12T15:19:50Z")
> [@](#): > > Quoth **TATG** : > > Was it the definition you had in mind? It’s phrased more cleanly than anything I had in mind, but it’ll do. ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [January 13, 2013, 5:27am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/31 "2013-01-13T05:27:42Z")
> [@CookingWithGas](#): > > Actually there are an infinite number of numbers between 1 and 2. True, but none of them are really _whole_, if ya know what I mean. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [January 13, 2013, 6:03am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/32 "2013-01-13T06:03:23Z")
The OP asked about the real number line. Which makes things a bit tricky. If the question was about the natural numbers, the answer would be no. It the question was about the integers, the answer would usefully be zero. **CookingWithGas** provides the neatest definition. However you can also start with zero and provide by construction the integers centered on zero, which is also neat. The rationals can follow, and thense the algebraics. Which pretty much gets us all the numbers we can construct. All centred on zero. Whether you consider this enough is another matter. We are left with the non-algebracis, of which there are rather a lot. So we have not constructed all the real numbers. You might argue that all the non-algebraics lie between rationals, and thus between integers, and thus are constrained, in distance from the middle, and thus zero is still a valid centre to the reals. ---
**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:** [January 13, 2013, 2:48pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/33 "2013-01-13T14:48:49Z")
> [@Maserschmidt](#): > > True, but none of them are really _whole_, if ya know what I mean. I know what ya mean but who was talking about whole numbers? ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [January 13, 2013, 7:49pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/34 "2013-01-13T19:49:19Z")
Nobody. Now run along with your serious answers. ---
**Author:** ![blueblonde](https://avatars.discourse-cdn.com/v4/letter/b/a88e4f/32.png) [@blueblonde](https://boards.straightdope.com/u/blueblonde)\ **Post date:** [January 14, 2013, 10:16am UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/35 "2013-01-14T10:16:01Z")
Infinity is not a number, it’s an idea, therefore it has no middle. I know that’s a sucky answer, but it’s true. ---
**Author:** ![Alka\_Seltzer](https://avatars.discourse-cdn.com/v4/letter/a/c89c15/32.png) [@Alka\_Seltzer](https://boards.straightdope.com/u/Alka_Seltzer)\ **Post date:** [January 14, 2013, 12:56pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/36 "2013-01-14T12:56:41Z")
_Middle_ is a concept, not a thing. The precise middle of a physical object can never be precisely defined. Where is the middle of a star, a car, a person, or an atom? ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [January 14, 2013, 1:36pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/37 "2013-01-14T13:36:05Z")
> [@Alka\_Seltzer](#): > > _Middle_ is a concept, not a thing. The precise middle of a physical object can never be precisely defined. Where is the middle of a star, a car, a person, or an atom? First, how is this relevant? You’re the first person to bring up physical objects in this thread. Second, what do you mean by “can never be precisely defined”? Why can’t I define the middle of a person as their center of mass, or their center of volume, or the spot where their bellybutton is? ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [January 14, 2013, 1:41pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/38 "2013-01-14T13:41:15Z")
I assume **Alka Seltzer** was rebutting the idea that _middle_ can’t apply to infinity. Middle is a concept here, but so is the extent of the real number line. In neither case does the need to apply concepts to physical things appear. Applying concepts to concepts is reasonable and yields useful answers, rebutting **blueblonde** ’s answer. ---
**Author:** ![Alka\_Seltzer](https://avatars.discourse-cdn.com/v4/letter/a/c89c15/32.png) [@Alka\_Seltzer](https://boards.straightdope.com/u/Alka_Seltzer)\ **Post date:** [January 14, 2013, 2:49pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/39 "2013-01-14T14:49:00Z")
> [@Thudlow\_Boink](#): > > First, how is this relevant? You’re the first person to bring up physical objects in this thread. Because the question is really one of definition. Concepts are useful, but they often have no actual basis in reality. > [@Thudlow\_Boink](#): > > Second, what do you mean by “can never be precisely defined”? Why can’t I define the middle of a person as their center of mass, or their center of volume, or the spot where their bellybutton is? It’s impossible to measure the middle of anything precisely, only approximate it (admittedly, to a high degree of precision), or provide an _arbitrary_ definition, as you have done above. It’s not useful or precise to define the middle of a person as the location of their bellybutton. You could only approximate my centre of mass, it varies from moment to moment due to the action of my circulatory and pulmonary systems. It’s not even possible to locate the centre of an atom exactly, due to the uncertainty principle. > [@Francis\_Vaughan](#): > > I assume **Alka Seltzer** was rebutting the idea that _middle_ can’t apply to infinity. > > Middle is a concept here, but so is the extent of the real number line. In neither case does the need to apply concepts to physical things appear. Applying concepts to concepts is reasonable and yields useful answers, rebutting **blueblonde** ’s answer. Exactly. There are some definitions of “middle” which can be applied to infinity. If you assume the real number line has the same number of positive and negative values, then the middle is zero. It seems intuitive, but I can’t find any proofs online. But is that a useful definition? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 14, 2013, 3:51pm UTC](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818/40 "2013-01-14T15:51:21Z")
> [@](#): > > If you assume the real number line has the same number of positive and negative values, then the middle is zero. It _does_ have the same number of positive and negative values, and in fact that’s easy to prove. But that’s not enough, since it also has the same number of values above and below 1, or above and below -57896210984.1789264, or any other number you choose. [Previous page](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818.md?page=1) [Next page](https://boards.straightdope.com/t/math-question-is-there-a-middle-number/646818.md?page=3)