Average of Infinity: Is It Possible?

In summary: You can get a sense for what happens though just by using the average of those two numbers (505) and then taking the limit as the number of workers goes to infinity. The limit would be the average of the infinite set, which in this case is also 505.In summary, the problem presented is to find the average salary of an infinite number of workers, with each worker's salary being a real number between 10 and 1000. This presents a challenge as the traditional method of averaging by adding up all values and dividing by the number of items is not possible in this scenario. However, a median point of 505 can still be used as a statistical indicator of the group's position. The concept of infinity is not necessary in this
  • #1
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Hello
I was watching lectures on Quantum Computing another day and I came up with a problem. I talked to my school teachers about it but everyone seemed to dodge my question except for one, my math team teacher who told me that without assuming anything it cannot be solved. Or we can take the lowest possible value and the highest, divide by 2 and that would be the average, or at last get 100 workers out of infinity and that would make an average of all.

Here's the problem:
What is the average of salaries of infinite number of workers, knowing that their salary can be any real number between 10 and a 1000?

What do you guys think about it?
Is it possible to solve it in any way? Or at least dig the problem to "average in terms of something"?

Thanks :)
 
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  • #2
This looks like a definition problem. In arithmetic, you average a group by adding up all values and dividing by the number of items. If you cannot add up the values and divide by their count then you cannot calculate the average. In your scenario, adding the values is impossible since you don't know them all. Dividing by infinity is also impossible, at least arithmetically. If you try to use a notion where it does not apply then you will have problems: what is the average color of a traffic light?

The purpose of an average value is to give a statistical indicator of the position of a group of values. Here, a median point (505) gives you a fair idea of where your group is located and this may be suitable for your purpose. Considering that the set of real numbers is infinite in both directions, this position extimate can even be considered highly accurate relative to the entire set. You just use the means you need to use in order to achieve your particular purpose and disregard what does not apply.
 
  • #3
If each worker's salary is independent of the salaries of other workers, you don't need to look at an infinite number of such workers. You only need to look at one.

- Warren
 
  • #4
So what is the average of infinity and one? Infinity?
 
  • #5
Infinity is not actually a number, so expressions involving infinity won't necessary behave like those involving real numbers. If you define an average as a sum divided by two, (infinity + 1)/2 = infinity.

- Warren
 
  • #6
You have not given enough information. You also need to give the distribution function. I'm guessing you will say all salaries are equally likely. That would be called a uniform distribution. In that case it is indeed 505. No considerations of infinity are needed. As chroot said, if you asked What is the expectation value for just one salary, it would also be 505.
 
  • #7
You can deal with the infinities just by taking limits as your number of workers goes to infinity. However, unless you're told some kind of distribution for the salaries, you've no idea other than it's going to be somewhere between 10 and 1000.
 

1. What is the concept of "Average of Infinity"?

The "Average of Infinity" is a mathematical concept that refers to the average or mean value of an infinite set of numbers. It is often used in theoretical and abstract mathematical calculations.

2. Is it possible to calculate the average of infinity?

No, it is not possible to calculate the average of infinity. This is because infinity is not a number and cannot be represented in a finite form. Therefore, it is mathematically impossible to find the exact average of an infinite set of numbers.

3. Can the average of infinity be approximated?

Yes, the average of infinity can be approximated using mathematical techniques such as limits and integrals. However, the result will always be an approximation and not the exact value.

4. Is the average of infinity always infinite?

Not necessarily. The average of an infinite set of numbers can be finite or infinite, depending on the values in the set. For example, the average of the set {1, 2, 3, ...} is infinite, while the average of the set {1, 1/2, 1/3, ...} is finite.

5. What are the real-life applications of the concept of "Average of Infinity"?

The concept of "Average of Infinity" has practical applications in fields such as physics, statistics, and economics. It is used to model and analyze infinite systems and phenomena, such as the behavior of particles in physics, the distribution of wealth in economics, and the probability of events in statistics.

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