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.
Somewheres between 0.999… and 1.
I read that here in GQ. It was a simple thread.
1 is a middling number, often. Oh. Never mind.
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.
Are you talking about my nephews?
Actually there are an infinite number of numbers between 1 and 2.
Well, I guess Somebody had to say it! 
All numbers are middle numbers.
It’s phrased more cleanly than anything I had in mind, but it’ll do.
True, but none of them are really whole, if ya know what I mean.
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.
I know what ya mean but who was talking about whole numbers?
Nobody. Now run along with your serious answers.
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.
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?
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.
Because the question is really one of definition. Concepts are useful, but they often have no actual basis in reality.
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.
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?
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.