Counting on a computing system

In summary, the conversation discusses the limitations of classical and analog computers in counting natural numbers and the concept of counting up to infinity. It also mentions the possibility of a machine that can count up to infinity, but no specific references are provided.
  • #1
thidmir
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TL;DR Summary
I'm looking for any references on a device that is capable of counting over the set of natural numbers
It is plretty clear that a classical computer can't count over the set of natural numbers. If it is a digital device and you used an infinite loop you would eventually run out of memory space and have to reinterpret the meaning of the numbers (so it isn't really counting independently). An analog device can't either because even if you had an analog function like 1/n, you would need a sensitive enough detector to distinguish large enough values of n which goes against the Uncertainty principle. I've heard of some people trying to develop a machine that can count up to (though not including) infinity but does anyone know of any specific references?
 
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  • #2
You cannot physically count all the natural numbers. You can only do it mathematically.
 
  • #3
thidmir said:
I've heard of some people trying to develop a machine that can count up to (though not including) infinity
It would count up to ##\infty - 1##? How is that even possible? What is the value of ##\infty - 1##?

A machine that would count to ##\infty - 1## would never stop until the end of time. And, at that time, couldn't we say that if it was built just 1 second earlier, or could have counted a little bit faster, that it could have counted at least one extra number?
 
  • #4
thidmir said:
I've heard of some people trying to develop a machine that can count up to (though not including) infinity
I have not, so I'd be grateful for any links ...

Your theme is quite interesting, though. But it makes me wonder: what exactly is counting? After a while just pronouncing the numbers would take endlessly long, so would it go towards an infinity squared business?
And how much is infinity minus half of that? So how long to count that?

## \ ##
 
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thidmir said:
I've heard of some people trying to develop a machine that can count up to (though not including) infinity but does anyone know of any specific references?
If you've "heard of" it then you should be able to give at least one specific reference. If you can't, and apparently you can't, then we don't have a valid basis for discussion.

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1. What is the purpose of counting on a computing system?

The purpose of counting on a computing system is to accurately and efficiently perform mathematical calculations and data analysis. This can include tasks such as counting, sorting, and performing complex algorithms.

2. How does a computing system count?

A computing system counts by using binary code, which is a system of representing numbers using only 0s and 1s. The system uses electronic circuits to process and manipulate the binary code, allowing for fast and accurate counting.

3. What types of computing systems can perform counting tasks?

There are many different types of computing systems that can perform counting tasks, including desktop computers, laptops, smartphones, and even specialized devices such as calculators and supercomputers. Any device that has a processor and the ability to process data can be used for counting.

4. Can a computing system count infinitely?

Technically, a computing system can count infinitely as long as it has the necessary memory and processing power. However, in practical terms, there are limitations to how high a computing system can count due to factors such as hardware limitations and the amount of time it takes to process each count.

5. How does counting on a computing system differ from counting manually?

Counting on a computing system is much faster and more accurate than counting manually. This is because computing systems can process large amounts of data at once and do not make human errors. Additionally, computing systems can count in different bases, such as binary or hexadecimal, which is not possible for humans to do manually.

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